Communism is a Dictatorship. Think Cuba. The leader is the only person in charge and he answers to no one.
Marxism is A view Point. Its a ideal that shapes how you see the world and what you do about it.
Marxism is an idea that people are supposedly equal, but communism is a government where most of the people are equal but they have a higher class who rule.
Communism is the communal ownership of property. Marxism is based on the theory of Karl Marx with government owning all property. A commune can exist in a democratic society.