I don't think it's a definition thing. I am US based but I've actually spent much of my life in Europe and my entire family lives there. Rural hospitals are not urgent care centers or health clinics. They're smaller but they're 100% real hospitals in the sense that both Americans and Europeans (at least in Spanish) use that word. They have 24/7 emergency care and can deal with serious health problems. However, they're not all "trauma centers." Trauma centers are a network with different nodes of various "levels," and different hospitals are certified at different levels of trauma care. There's usually only a couple of "level 1 trauma centers" in a region.