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’ve never once heard an American use the term “village” to describe a municipality, even ironically.
It’s dependent on a given state’s terminology. New York, for example, has villages. They’re municipalities that fall within towns, but collectively offer additional services that the town does not. So I could live in the village of Pomona, in the town of Haverstraw, and I’d need to pay taxes to the village and the town separately.