Is there a query language variant of Turing Completeness?

By this I mean a theory where you can say Language X is Query Complete so that you know that language is able to do any sort of query? I’m guessing not because some queries would run into things that a language would have to be Turing complete to work?

Why do I wonder – well you might have a relational database and a graph database and someone might say anything that can be done in the relational database can be done in the graph database (albeit at different speeds) so I would like if there were some terms DB A and DB B are both Query Complete – or if not that if there was a way to categorize levels of "query completeness" (I’m just going to assume my ill defined concept is totally understandable to everyone) so one can say stuff like "DB A is query level 4 but DB B is at query level 3, but of course much faster because of those limitations."

I sure hope (so as to not feel like a bigger idiot than normal) that the answer to this question isn’t just a flat No.