>People in the US tend to think it refers to things that are actually mixed economies or primarily market economies with strong social guarantees. Think things like the Nordic model or the European model...
Yes. This is what people in the US mean when they say socialism in general conversation. They don't mean pure Socialism as Marx talked about it. Similarly when people say the US is a democracy, we know they don't mean it's an actual pure Democracy where everyone votes on every issue.
Yes with the pedantic caveat that those aren't similar in the sense that one is a common confusion and the other is correct.
The Nordic model is the sort of economy and political structure that the 19th century socialists explicitly reacted against and rejected. It's a representation of mainstream liberal democratic theory not of socialism.
On the other hand democracy was always understood to be representative because you can't make every decision by plebiscite.
It has to do with being accurate rather than being "pure".
These particular words haven't evolved in any meaningful way in the last century or so. If anything socialism now refers exclusively to revolutionary/militant utopian socialism whereas it had more varied meanings long ago. That's probably largely an artifact of the fact that socialism since the early 1900s has mainly been promoted by socialist countries after a revolution.
Go on a socialist forum and ask them what they think about markets or mixed economies. E.g.
Yes. This is what people in the US mean when they say socialism in general conversation. They don't mean pure Socialism as Marx talked about it. Similarly when people say the US is a democracy, we know they don't mean it's an actual pure Democracy where everyone votes on every issue.