Oh please!
Let's not start endless recollections of "I once had a vomiting pax in my little Cessna and I did/didn't declare
[choose one](emergency/pan/pan medico/mayday). This discussion is about the nuances of emergencies and how to declare them. We all know that ATC will do what they can to expedite a routing/arrival if there is a problem. The main point here is what words trigger their reaction and what mental thumbscrews they will apply to you in the UK if you don't use the magic word.