Wikipedia isn't a dictionary. Good try, though.
Marx states that the only way to solve these problems is for the working class (proletariat), who according to Marx are the main producers of wealth in society and are exploited by the Capitalist-class (bourgeoisie), to replace the bourgeoisie as the ruling class in order to establish a free society, without class or racial divisions.
Communism is a social structure in which classes are abolished and property is commonly controlled, as well as a political philosophy and social movement that advocates and aims to create such a society.
In modern usage, communism is often used to refer to the policies of the various communist states, which were authoritarian governments that had centrally planned economies and ownership of all the means of production. Most communist governments based their ideology on Marxism-Leninism.
Did you just try to CTRL+F "Communism is a Government" or what?
EDIT: Seriously, let me spell out the difference for you. From Wikipedia:
Socialism is an economic and political theory based on public ownership or common ownership and cooperative management of the means of production and allocation of resources.
Communism is a social structure in which classes are abolished and property is commonly controlled, as well as a political philosophy and social movement that advocates and aims to create such a society.
Communism incorporates Socialism. They are not the same thing. Communism can't really exist
without Socialism, but Socialism can exist without Communism.
Of course, this sort of logic puzzle often trips people up (though, I've never had trouble with it), so I fully expect you to not to understand and claim that I've proven you right. That's fine, you can do so all you like. Just make sure you provide an URL to this post every time you do. The people who actually understand are the ones I want to talk to on the internet, anyway.