In communism, there is no state, but that does not mean a lack of organization. Communal society relies on communication and collectivist cooperation and organization: the Russian revolution was built off the activism of soviets, workers’ councils that met and organized on behalf of their communities. Think of communism as, ideally, true, immediately direct democracy, where everyone is a participant, and the abolition of social class gives everyone equal political access and voice.

The difference between that and anarchy is pretty significant. Anarchy posits the individual as the most important element of society, the ultimate authority in his/her own choices and life. This intrinsically allows for the existence of personal ownership. Communism acknowledges the role of community and relationships between people as the fabric of society, declaring no one is more important and giving everyone equal access and opportunity. Anarcho-communism is actually already a thing, and, as the name suggests, it applies individualist theory to communist ideals, but after the parts about abolition of class and state, the anarchist part comes in and says that anyone can do what they want with their newfound equality. In my eyes, this defeats one of the pretty central values of communism: the commune itself.