Collectivism holds that the individual is not an end in oneself, but is a tool to serve the ends of collective.
“The political expression of altruism is collectivism or statism, which holds that man’s life and work belong to the state—to society, to the group, the gang, the race, the nation—and that the state may dispose of him in any way it pleases for the sake of whatever it deems to be its own tribal, collective good.” — AYN RAND 
Collectivism holds that the individual is not an end in oneself, but is a tool to serve the ends of others (the collective). Whereas, individualism declares that every individual should live their life for their happiness, as an end to oneself; collectivism holds the group as the primary and the standard of moral value. Whether that group is a dictator’s gang, the nation, society, the race, the gods, the majority, the community, or the tribe is merely a matter of detail.
The individual’s moral purpose is as a sacrificial victim, whose value is the ability to sacrifice one’s life, liberty and happiness to the will of the group.
Statism is a political-economic system where the individual lives not by inalienable right but by permission of the state.
Where the political result of individualism is capitalism (a social system where the individual does not live by permission of others, but by inalienable right).
The political result of collectivism is some form of statism: a system where the individual lives by permission of the state.
Under statism, the government is no longer a paid political servant or policeman, but a master with the legal power to initiate force against legally disarmed citizens.
In particular form, many of these forms of statism differ superficially, but in theory, and bloodstained practice they all unite upon the same fundamental collectivist ethical principle: the individual is not an end to oneself but is a tool to serve the ends of others. Whether those “others” are a dictator’s gang, the nation, society, the race, (the) god(s), the majority, the community, the tribe, is irrelevant — the point is that the individual is not sovereign but a serf.
Only capitalism declares that every human being, may live their own life for their happiness, as an end to oneself, not by permission of others, but by right, and that government’s sole responsibility is to protect those rights and never violate them as they are inalienable. Statism declares that each individual exists to serve the state.
Socialism is a collectivist-statist form of government where the state owns the economic system leading to the eventual destruction of civilization.
A “socialist society” is one where the economy has been taken over (“socialized,” “nationalized”) and is now ruled (“managed”) by the state. Under socialism, all property is owned, controlled, and distributed by state central-planners.
Economically, socialism is a form of economic totalitarianism. Under socialism, the government dictates all economic decisions, including dictating “prices,” dictating the allocation of resources, dictating contracts, dictating jobs, etc. The opposite of a socialist, or command economy is a market economy or free-market (under capitalism).
As there is no private property under socialism, there is no basis for free-trade between individuals, and thus there is no market price system (except in the socialist country’s “black markets”), no market profits, or market losses, as there are no market participants — everything is owned and allocated by state “central planners.”
Without a rational price system (all prices are set arbitrarily by central planners) there is no means of rationally allocating capital (no profit-loss system to judge one’s efforts) leading to massive capital malinvestment in the long run. Without a market price-system and the profit and loss signals provided by market-competition, state “planners” end up misallocating resources (“planned chaos”) leading to the destruction of the economy in the long-run. This is the problem of the inability of “economic calculation” under all economic forms of socialism (See Ludwig Von Mises, Economic Calculation in the Socialist Commonwealth.)
Socialism leads to a destructive form of competition where individuals do not compete economically to produce values for trade but compete politically to expropriate the values produced by others.
Under socialism, political competition replaces the market competition of a capitalist society. Under market-competition, individuals organize to compete with each other to trade products/services in exchange for values (money) from others, i.e., freely trading value for value for mutual benefit. Under political competition, individuals organize to lobby economic dictators for favors (“cronyism”), with those with the most “political pull” receiving the proceeds at the expense of those who are forced to produce, i.e., “from each according to his ability and to each according to his need.” Those who are the most productive are judged to have “ability,” while those who are popular with state bureaucrats are judged to have the most “need.”
Thus, the profit motive (creation of wealth) of capitalism is replaced with the loss motive (plundering of wealth) of socialism. To quote economist Ludwig Von Mises,
“Socialism is not in the least what it pretends to be. It is not the pioneer of a better and finer world, but the spoiler of what thousands of years of civilization have created. It does not build, it destroys. For destruction is the essence of it. It produces nothing; it only consumes what the social order based on private ownership in the means of production has created.”
The government taking over the “means of production” has not only economic ramifications but political and legal ones as well. Since society, like the individual, is an inseparable whole the ramifications of the state “owning” the economy, have repercussions for the rest of society outside the economic sphere, i.e., where the state owns all the printing presses and radio stations, government bureaucrats end up determining the content of those newspapers and radio stations. So by enslaving the economic side of the individual, one ends up controlling the political/social side as well.
Politically, socialism is a form of statism based on the collectivistprinciple that the individual has no right to the results of their productive efforts (property) and the results of those efforts belong to and may be dispensed by “the collective,” as embodied by the state. This is the justification for the state taking over the “means of production.” As the right to property one has produced is the practical means of supporting one’s life, one no longer can be said to have a right to life in practice (but only in name, if that.) Thus, with no right to one’s efforts, one in practice has no right to one’s life, but in principle lives by permission (of the state).
Legally, socialism is a pure system of regulation and operates under a “rule of man,“ i.e., central planners, dictators, and bureaucrats. Far from being a classless society, individuals under socialism are divided into two groups: those who give orders (master) and those who obey (serf).
“When, at the age of twelve, at the time of the Russian revolution, I first heard the Communist principle that Man must exist for the sake of the State, I perceived that this was the essential issue, that this principle was evil, and that it could lead to nothing but evil, regardless of any methods, details, decrees, policies, promises and pious platitudes. This was the reason for my opposition to Communism then—and it is my reason now. I am still a little astonished, at times, that too many adult Americans do not understand the nature of the fight against Communism as clearly as I understood it at the age of twelve: they continue to believe that only Communist methods are evil, while Communist ideals are noble. All the victories of Communism since the year 1917 are due to that particular belief among the men who are still free.” — AYN RAND, Foreword to We The Living
Communism is a social (political-legal-economic) system based on the altruist-collectivistprinciple that the individual has no right to their own life, but has value only in regard to their selfless (altruistic) service to the group, commune, or collective.
Politically, communism is a radical form of statism that is totalitarian/authoritarian (for examples of the totalitarian nature of communism see The Black Book of Communism.) Whatever “freedom” an individual has under communism is not by inalienable right, but by revocable permission.
Legally, communism is a pure system of regulation and operates under a “rule of man“, i.e., central planners, dictators, and bureaucrats. Far from being a classless society, individuals under communism are divided into two groups: those who give orders (master) and those who obey (serf).
Like all forms of socialism, communism leads to a destructive form of competition where individuals do not compete economically to produce values for trade, but compete politically to expropriate the values produced by others.
Economically, under communism, since one does not have a right to one’s life, one does not have a right the results of ones productive efforts: property. Thus, under communism, all property is owned, controlled, and distributed by state central planners under the principle of “from each according to his ability, and to each according to his needs.” Economically, communism is pure socialism in principle — and practice.
As there is no private property under communism, there is no basis for free-trade between individuals, and thus there is no market price system (except in the communist country’s “black markets.”) Without a rational price system (all prices are set arbitrarily by central planners) there is no means of rationally allocating capital (no profit-loss system to judge ones efforts) leading to massive capital malinvestment. This is the problem of the inability of “economic calculation” under all economic forms of socialism (See Ludwig Von Mises, Economic Calculation in the Socialist Commonwealth.)
“[T]error has always been one of the basic ingredients of modern Communism. Let us abandon once and for all the idea that the execution of hostages by firing squads, the slaughter of rebellious workers, and the forced starvation of the peasantry were only short-term “accidents” peculiar to a specific country or era….”
“…[W]e have delimited crimes against civilians as the essence of the phenomenon of terror. These crimes tend to fit a recognizable pattern even if the practices vary to some extent by regime. The pattern includes execution by various means, such as firing squads, hanging, drowning, battering, and, in certain cases, gassing, poisoning, or “car accidents”; destruction of the population by starvation, through man-made famine, the withholding of food, or both; deportation, through which death can occur in transit (either through physical exhaustion or through confinement in an enclosed space), at one’s place of residence, or through forced labor (exhaustion, illness, hunger, cold). Periods described as times of “civil war” are more complex—it is not always easy to distinguish between events caused by fighting between rulers and rebels and events that can properly be described only as a massacre of the civilian population.”
“Nonetheless, we have to start somewhere. The following rough approximation, based on unofficial estimates, gives some sense of the scale and gravity of these crimes:
U.S.S.R.: 20 million deaths China: 65 million deaths Vietnam: 1 million deaths North Korea: 2 million deaths Cambodia: 2 million deaths Eastern Europe: 1 million deaths Latin America: 150,000 deaths Africa: 1.7 million deaths Afghanistan: 1.5 million deaths The international Communist movement and Communist parties not in power: about 10,000 deaths.“
“The total approaches 100 million people killed.” 
Racism is a form of collectivism that ascribes moral and political significance to an individual’s race and/or ancestry (instead of the individual’s choices/actions and their nature as a rational being.)
Writes Ayn Rand on the nature of racism:
“Racism is the lowest, most crudely primitive form of collectivism. It is the notion of ascribing moral, social or political significance to a man’s genetic lineage—the notion that a man’s intellectual and characterological traits are produced and transmitted by his internal body chemistry. Which means, in practice, that a man is to be judged, not by his own character and actions, but by the characters and actions of a collective of ancestors.” 
What is racism? Racism is a form of collectivism that judges an individual by their ancestral heritage/race, as opposed to one’s nature as a rational being. Racism stands in opposition to the method of individualism — judging each human being as an individual, i.e., by the content of one’s character and actions, and not by their skin color and ancestry.
Politically, the only protection an individual needs from racists is the protection of their rights — freedom from the initiation of physical force, whether it be a knife held at one’s throat by a Black Panther or the noose held by a member of the KKK. Capitalism is the only social system that “defangs” the political power of racists by banishing the initiation of physical force.
Observe the great American “melting pot” where the warring tribes of Europeans who were busy killing each other in Europe, were able to live relatively peacefully together when they moved to America. What principle was the cause of this? Politically, the principle of individual rights — the foundation of capitalism.
The principle of individual rights and its underlying individualism is being eroded as the new racists of today, who are advocating that some individuals be granted political privileges based on their skin color and ancestry, i.e., affirmative action, racial quotas, etc. Under capitalism, such racist policies — carried out by the power of government — would be outlawed.
Observe that a complaint about capitalism is that “all the capitalist cares about is money” in one sense is true when one observes that those who care about money regarding their business, care naught about the color of their customer/employee as long as they deliver payment/perform their job. Money and profit are color-blind.
Anarchism is a form of collectivism, where individual rights are subject to the rule of competing gangs.
Writes Ayn Rand on the nature of anarchy as a political form of organization:
“…a society without an organized government would be at the mercy of the first criminal who came along and who would precipitate it into the chaos of gang warfare. But the possibility of human immorality is not the only objection to anarchy: even a society whose every member were fully rational and faultlessly moral, could not function in a state of anarchy; it is the need of objective laws and of an arbiter for honest disagreements among men that necessitates the establishment of a government.”
Anarchism is not a form of capitalism; anarchism is a form of collectivism, where individual rights are subject to the rule of competing gangs.The only peaceful solution to such disputes is to have one agency with the power to settle those disagreements, according to one set of objectively defined laws — a government. This is what corporations do under capitalism when they have a dispute with each other — they go to court (government).
Some “anarcho-capitalists” (a contradiction in terms) suggest that “corporate organizations” would be able to provide the physical protection for their “customers” making government unnecessary.Those who advocate “anarcho-capitalism” seek to replace the rule of law, with a rule of the mob. The proper name for such an organization is not “corporations,” but street gangs, who fund their business through extortion of their victims (inaccurately called “customers”).
Government is a single agency with a monopoly on the power to legally use force in a specific geographic area. What “anarcho-capitalists” purpose are multiple agencies in the same geographic area, that have the power to use force subject to no rule of law.
For those who want an illustration of what happens when two ‘competing-governments’ are arguing with each other in the same geographical area, see: Bosnia. On a macro-level, the balkanized wars in Bosnia and Rwanda are the result of the anarcho-capitalist’s ill-thought-out nightmare: a species of collectivism, where one is subject to the whims of the tribe or gang in power.
On a micro-level one can observe anarchism in black markets, where drug dealers compete on the same “turf” to “protect” their interests. It is to subject “might” to “right,” that one requires rights, and that one requires a government to protect those rights.
Those who attempt to combine anarchism with capitalism, make the error of confusing the peaceful form of competition of capitalism — trade, ideas, and dollars — with the brutal “jungle” form of competition of anarchism — brutality, whims, and bombs.
What happens when one ‘corporate protection agency’ disagrees with another in the same geographic area? By what method do they solve their dispute? They do it by competition not with dollars, but with guns. They seek to solve their dispute by resorting to force against each other, i.e., a perpetual state of civil war. Under such a system, which gang wins? The gang that is the most brutal.
Anarchism is not a form of capitalism; anarchism is a form of collectivism, where individual rights are subject to the rule of competing gangs. Under such a system, any individual would beg for the relative safety of a dictatorship.