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).
Lots of villages in NH, although I don’t think it’s a legal term. For example, Wakefield NH residents seem to refuse to accept that they have a town. They refer to the legal township as “the villages of Wakefield”, and when asked their residency, will say “I live in the village of Union” (or Sanbornville, etc.) also, there is the village of Milton Mills in the town of Milton, and Gonic in Rochester.