As a non-American, I’m very confused by this. If it’s a town, it’s not rural by definition. Because, you-know, it’s urban.
Also, could we get a definition of town vs small town. Do you not have the concept of a village? (Village in the UK would be a settlement with a population of a couple of thousand, with usually a pub, local shop, maybe a post office and primary school if you’re lucky).
Alright, I’m fascinated. Ironically, all the villages I know are in NY, but more so NYC/Long Island and the immediate area. I don’t read many signs north of there because the trees look too damn pretty when I visit. I assumed they were legacy names but I’m probably standing corrected