What is communism? Stripped down to its barebones, that is. No baggage. No carxism. No anarcho-communism. Communism is a form of socialism, which is set of economic systems where the holders of the means of production and the producers are one in the same, in which the workers rise up in revolution in order to create a society without class, money, or a state.
What does marxism add? Marxism adds a couple of things. First, it adds party politics. According to marxism, communists should form political parties and participate in the political system until they can successfully revolt. In addition, that party continues after the revolution. Second, it adds the transitional period. The transitional period is a period of statism where people "learn" to be communists. Which leads to the third thing it adds, the dictatorship of the proletariat. According to marxist theory, the narxist party would form a dictatorship of the proletariat in the transitional period to help the people adjust. This is supposed to fade away as it becomes unnecessary.
Now, this is different from anarcho-communism. How so? Anarcho-communism adds very little to communism. There is no parties. There is no transitional period. There is no dictatorship of the proletariat. Anarcho-communism is immediate after the revolution. We abolish the state right off the bat and socialize everything right off the bat. All that's really added is self-governance through direct democracy.
Ok, but why not marxism? The theory seems sound, so why reject it? Quite simply, the transitional period does not work. More accurately, it never ends. The dictatorship of the proletariat becomes a totalitarian regime that refuses to give up power. This is what led to stalinism and maoism and every other mommunist regime around the world.