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).
See also: census designated places, a collection of people with no formal town incorporation/government. My dad grew up in a “town” (CDP) of about 250 residents. It’s about a half hour drive from the nearest real town, for things like groceries and hospitals.