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).
I only know about the existence of villages in NY state because my brother lives in one and had to explain to me what constitutes a village vs. a town–I still don’t really get it! - which is why I said the term may have a more specific definition. So yeah, it may not be a commonly used or understood term even in the NE. In any case, I’m sure it’s used differently here than in the UK, like many things.
We have cities named “Village of St Anthony”. I guess it’s to be quaint