Communism is the view that property should be owned collectively—that, in other words, there should be no such thing as private property, at least not on a commercially meaningful scale.
Marxism is something very different from communism. Marxism is the view that our beliefs about the world, and also about morality, are rationalizations, and therefore falsehoods, that are based, not on objective fact, but on propaganda put out by the people who own the means of production. Thus, Marxism and communism are completely distinct doctrines.
In this short work, it is explained how, despite their differences, Marxism and communism are connected.
An Author's Republic audio production.