Communism: A form of socialism that abolishes private ownership; a political theory favoring collectivism in a classless society.
Socialism: A political theory advocating state ownership of industry; an economic system based on state ownership of capital. (from wordnet.princeton.edu/perl/webwn)
These are two very good definitions of socialism and communism. People have twisted the ideas of communism and socialism to hide their true faces from the public, whom they hope to seduce into slavery with both of these political traps. Communism is portrayed (though not always by that name) as perfect equality. Socialism is portrayed (though not always by that name) as government protecting and helping you because it can do it better than you. Meaning that it is superior to you. Which is different from what they say communism is, in fact, quite the opposite. They seem incompatible. But they are inseperable.
Imagine a classroom in which the teacher gives to every student the same grade, regardless of how they did on the test. That is communistic socialism. There is perceived equality, but notice that the teacher is separate from the class: socialism. The difference between socialism and communism is mostly just focus. Communism is the students each getting equal grades; socialism is the teacher overstepping his bounds and arbitrarily controlling the grades to match what he wants. Both are bad situations.
Watch out for sophistry. Especially in semantics.