The rat difference isn’t the where they live so much as their lifestyle — one is nocturnal, the other one (the one seen walking along the sidewalks in large NE cities in the US) isn’t. :’)
I have seen plenty of nocturnal gray (Norwegian) rats in NE US cities. I occasionally see one in daytime, but usually it is young, or sick. I was once walking at night when a huge rat looking creature ran in front of me. I screamed, but then realized it was an urban opossum. I once read that 17 western states had endemic bubonic plague among their rodents, especially the prairie dog colonies.