Anarchism aims for a communist society ultimately. With the difference between Marxism and Anarchism being, that Marxism aims for a temporary "dictatorship of the proletariat" which is supposed to wither away eventually and turn into a classless society, while Anarchism wants to skip that part and immediately abolish any kind of hierarchies and reign of one over another. And given Marxist-Communists history so far, Anarchists were kinda right when saying that power corrupts and once a group (in this case the working class) gains political power and sovereignty, they wouldn't just abolish it.
I would like to mention two more things, anarchists believe in prefiguration ( building the new in the shell of the old ), and in means ends unity
Prefiguration means that the revolution is not an event that takes place where a state imposes socialism from the top down, but that workers themselves must build the new institutions that they wish to replace the old ones with
For example, making unions to build up the power of workers, it's revolution from the bottom up, imposed by those at the bottom on those at the top
As I understand it, prefiguration is also how capitalism appeared, where capitalist institutions were formed and slowly overtook feudalism
Means ends unity means that the means used determine the ends that are achievable
If my goal is to move one meter to the north, I can not achieve that by moving one meter to the south
Means ends unity would say that if you want to get one meter north of your current location, you must move one meter north, the ends desired determine the means that can be used to achieve them
And the means we use determine the ends we can achieve
Means ends unity is also completely opposed to the "ends justify the means" idea, as it says tyrannical means lead to tyrannical ends
Worker ownership is achieved by giving workers ownership, not by giving a state ownership, like state socialists do