If a person is a Marxist, do they support Communism?

I've seen many people claim to be Marxist (one of those persons is Christopher Hitchens) and I'm a little confused when they use this term. I know that it's an idea from Karl Marx, but does Marxism necessarily mean communism? If someone if is living in a western democratic society and claims to be a Marxist, they're against Capitalism, correct? But then if they're anti-capitalist, why live in a capitalist society? Is it because most communist nations don't have the freedoms that western societies have? Please enlighten me.