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).
To my knowledge, US states may use different terms for municipalities, collections of homesteads, etc. as they wish because of the 10th amendment in the US Constitution, i.e. it’s not explicitly given to the fed government to prescribe the hierarchy. But I’m no expert on this subject, so I could be mistaken.