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Communism has nothing to do with equality. Communism is an ideology based on historical materialism which wrongly concludes that a capitalist system is intrinsically exploitative. It promotes class warfare and the establishment of a dictatorship of the proletariat, which in practice means that economic activities need to be planned by a central authority. It is a totalitarian and collectivist movement.
Marx or Lenin have never talked about "equality"; this is just some bullshit that boomer MAGAtards believe because they can't see the difference between Lenin and Bernie Sanders.

Modern liberalism is an ideology which puts the individual above society and promotes democracy and equality, equality meaning that every single aspect of an individual needs to be made equal - e.g. a homosexual needs to be *equal* to a heterosexual. But modern liberalism is happy with economic inequalities and it believes in a market economy, with some exceptions such as "diversity" and "sustainability".

I could write a whole fucking essay. They are so different that they have basically nothing in common.

In a nutshell communism is about a different economic system, modern liberalism is about equality in everything *except* the economy. In America today a CEO makes 200 times what the average worker of his company made. Does that look like communism to you?