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).
NY has towns and villages. A township is way larger than a village. For example the Town of Huntington vs the incorporated Village of Lloyd Harbor within the town. We also have hamlets, like Huntington Village, which are similar but unincorporated.
However, all of this I’d consider suburban, not rural.
Sometimes the village within the town even has the same name, like Batavia and Albion