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).
A town in the USA has a population requirement of at least 5,000 people. However that can be spread out over hundreds or even thousands of square miles.
Villages do exist (I live in one) and it is generally defined as a smaller incorporated entity within a town.
So, for instance, I live in the country of the USA, in the state of New York, in the county of Allegany, in the Town of Andover, in the Village of Andover. It’s like nesting dolls of government and taxes.