> Socialism and communism is about collective ownership of the means of production (or lack of private property, which is basically the same, ie is everyone is super none is). This would mean that the means of production are owned collectively by society.
Yes, correct.
> If this is correct, then how is state socialism supposedly not socialism, since the state, and by extension society, given that the state or "state-but-not-called-a-state" is democratic, is everybody? Is a situation wherein society as a whole controls the state (worldwide state, federation, syndicate, what have you) and thus means of production, not socialism? It does not have classes, since there is no one who owns or controls the means of production more than the other. There is no private property, since all means of production are owned collectively and democratically by society. It seems to me that state socialism, by this definition, would actually be socialism. In my opinion, it would even be more democratic than lots of independent communes trading between each other, which is what I saw people claim to be socialism or communism.
Essentially, yes - socialism can have an organizational, representative, democratic body that functions like a "state" in many respects, but it is important to acknowledge that it is NOT a "state" in the technical sense.
> Am I totally off the path here? Did I make an error? Or is it simply the case that the term "state socialism" has been smeared by state despotism (IE ruled by a few and not society, a-la Stalin and most famous failed left-wing states).
You're not totally off any path, really. The issue is precisely as you say, almost a semantic one. But we can't ignore it, either; the words we use to describe things affect our understanding of that thing, and our understanding of things affects our behaviour.
There is a big difference between "a state-like organisation in a socialist world" and "the state" in all historical and present societies. That is why they are distinguished.
I'd recommend reading "The Origin of the Family, the State, and Private Property" by Engels for more questions on the origin, and the trans-historical function, of the state, in order to better understand why such a distinction is necessarily made.