Communism is State Socialism. It should be wrong to say that it is the only socialism out there, but it is definitely socialism.
Nonsense. Read your Marx. Communism and Socialism don't even remotely resemble one another. The only reason people get them confused is that Communism, as defined by Marx, was the ideal human goal and has never actually existed.
What you describe as "State Socialism" is what most people just call Socialism... because socialism requires a strong State.
While some countries liked to CALL THEMSELVES communist, they were not. They were anything but. The best any of them ever managed to achieve were bad forms of socialism and fascism.
The reason for that is simple: socialism (the real economic theory of socialism) requires a strong central authority. Whereas communism (genuine communism, according to social and economic theory) has no "authority" at all.
The problem has been that once a relatively few people got all that authority, under a socialist or fascist regime, they then never wanted to give it up. So societies never "evolved" beyond that to true communism. Nor is it likely to ever happen. Marx was a loon.