Just FYI, the 2 parent comments are completely wrong and you shouldn’t remember these definitions.

Socialism = means of production are owned by society, but classes still exist (the working class rules over the former bourgeoisie)

When that process is finished and classes and contradictions that lead to them have been completely abolished, that’s communism.

Which is the same society that Anarchists want to achieve, the only difference is that Anarchists don’t have a coherent plan on how to get there.