[1]Granted, I'm thinking of European definitions here, because I get really confused when I try to educate myself about American ones. An GmbH is more or less an AG with stakes rather than shares, whereas an American LLCs seem to behave somewhat differently (taxation, for example is pass-trough).
It's not really a union of assets nor people though. The former would be a trust or arguably a non-profit, and the later would be a partnership. And LLCs can elect to be taxed as a C corporation, although I can't fathom why one would. (And most small businesses can elect pass-through taxation!)
I also would not refer to an LLC as a collection of assets for a common purpose; instead I would say it is a popular entity form that limits member or manager liability. However you could take a different view.