I think there are different definitions of what a union even is. German here and I was really quite surprised to understand that unions in the US are apparently per company. I believe in most of the EU, unions are per business sector - so while unions are in a sense stakeholders of the companies (if the company goes bust, it can't provide jobs), it usually doesn't have a specific interest in keeping employees in a particular company.

American unions have 'shops', which often correspond to companies. But sure America has national unions. Most of them are.

I've always heard "shop" used in relation to a particular business being union or non union in terms of who they hire (i.e. "they're a union shop" means they'll only hire IATSE or something like that and no non-union people), and "locals" being the actual union you belong to, but that's from the theatre world which might be a bit different.

Ah, that makes sense, then I might have misunderstood.

So does that mean, when the headlines say "Amazon workers (from a particular warehouse) vote to unionize", it's really about bringing that warehouse under the umbrella of an existing union?

Oftentimes, yes. They could form their own union but it's common to join an existing union.

Having universal or near universal union membership for a certain profession is limited to certain jobs, things like warehouse workers or retail employees aren't anywhere near that.