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).
“Village” isn’t used anywhere in the USA as far as I know. Places with <500 people call themselves a town usually. Where I’m from in NH (close to these towns), residents call themselves townies. “Small” is kinda just used as a grammatical intensifier in all the cases I’ve heard it used. YMMV in the south or Midwest though.
https://en.wikipedia.org/wiki/Village_(United_States)
The term village is used to describe certain categories of populated areas, either colloquially or legally, in 27 states.
Villages are quite common in the north eastern US.