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 grew up in a village in Ohio, population around 350, which was pushing the numbers honestly. Around 1000 is a town I think.
A nearby “city” is constantly in and out of city status. They always try to bump the numbers because city status means more funding. They are around 25000 pop.