Edit to add: I think I see what you meant now. Yes, you could also say “socialism is a movement toward communism,” in the sense that socialism is a step in the path to communism.
I don’t think so. Communism can’t be reached in one fell swoop. The reason why communist states didn’t and don’t have communism in their names is because—by their own admission—they aren’t yet communist, they’re socialist.
First comes a transformation from a dictatorship of the bourgeoisie to a dictatorship of the proletariat, where the working class has control of the state and the means of production. In other words, socialism. The end-goal of communism is to be rid of classes altogether, but it’s not possible jump straight to it. You can’t go to bed one day under capitalism and magically wake up the next under communism.
Marxists define the state as a system by which the ruling class maintains its dominance other classes. So when we talk about the end-goal of a “classless, stateless society,” we mean that classlessness definitionally also means statelessness.
