They're different names for slightly different but similar animals like the Germans using Kaninchen Vs Hase for rabbit vs hare

"Wasp" is an entire family of insects; there are a bunch of them. Where I live, we do have both yellow jackets and hornets (and call them as such), but when somebody says "wasp" they're typically referring to a red paper wasp (this or this -- I was unaware there were two different kinds until just now, BTW).

Wasp, colloquially, is a general term for stinging insects including yellowjackets, bald face hornets, and paper wasps. I have all 3 around my home but primarily yellowjackets and admit I revert to the general term often. It could be a regional dialect habit, my apologies.

I do appreciate all of the information people are giving about how they are handled in Europe. For what it is worth, we do have someone in the home with an allergy bad enough to have an EpiPen always with them. We only clear their nests from the deck (outdoor platform attached to home where we eat/lounge outside during nice weather) or around the front door. I will look into finding a service that will remove them humanely in the future.