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).
In geography academia, “small town” usually means a place that has a name and between 5000 and 50000 inhabitants. Though I suspect that a large part of the confusion here is that a lot of US towns are very low density and don’t have anything like a center. So those towns are themselves rural in look and feel, regardless of total population.