Politically, a capitalist is an advocate of laissez-faire capitalism, regardless of how rich or poor they are.
The words capitalism and capitalist are used in two different but related senses: one in a compartmentalized sense within the specialized science of economics (that studies the nature of production in a division of labor society), the second in a wider sense in the encompassing science of politics (the branch of philosophy that examines the fundamental nature of social systems).
Within the specialized domain of economics, a person who invests capital in a business concern is recognized as a capitalist, regardless of whether he advocates capitalism politically or not, e.g., Frederique Engels, Warren Buffet, and George Soros are economically capitalists.
More broadly, that is philosophically and politically, only an advocate of laissez-faire capitalism is as a capitalist, e.g., philosopher-novelist Ayn Rand is politically a capitalist, factory-owner Frederique Engels (and co-author with Karl Marx of The Communist Manifesto) who advocated communism is politically anti-capitalist.
Though economically Engels came from a wealthy background, politically he is recognized as a socialist/communist because of his ideas.
Similarly, billionaires Warren Buffet, Ted Turner and George Soros — can be economically compartmentalized as capitalists — but philosophically they are not capitalists as they do not advocate capitalism on principle, but are advocates of “mixed economy” statism (capitalism combined with anti-capitalist elements) to various degrees. Soros being more anti-capitalist than Buffet.
Soros, like billionaire Ted Turner, is a “socialist at heart.”