Marxism implies a specific mode of analysis and historical perspective while anarcho-communism is primarily a political tradition and mode of organization. Both have unique histories, normally as allies, but also enemies in some context.
Historically, Marxists and anarchists have primarily disagreed upon the usage of a state in a "transitional period" from bourgeois society into communist society. Bakunin and other anarchists of the first international era dismissed the transitional period on the basis that the society resulting from this route would essentially resemble bourgeois society and would be characterized by lack of autonomy for the worker. Marx, Engels, and the so called "authoritarians" of the first international dismissed the abolition of the state on the basis that revolutionary suppression of the bourgeoisie and abolition of property necessitates the existence of a state until these things have been completed then the existence of the state becomes "superfluous".
"The people have proved that they can run it... They (the pigs) can call it what they want to, they can talk about it. They can call it communism, and think that that's gonna scare somebody, but it ain't gonna scare nobody" ― Fred Hampton
“Mao Zedong said that power grows from the barrel of a gun. He never said that power was a gun. This is why I don't need no gun to do my thing. What I need is some freedom and the power to determine my destiny” ― Huey P. Newton