That’s socialism, right?

The Marxist definition of socialism is that the government owns the means of production. That definition prevailed during the Cold War when you had such socialist countries. Communism is a utopian state which is promised to come after socialism. It's the system of a post-scarcity society where you don't have property because everything is abundant. The state withers away because it is no longer needed. Basically, it's a society like in Star Trek. In Marxist thought, the development is: feudalism->capitalism->socialism->communism

Of course, it's not wrong using the term "socialism" more loosely.