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).
The use of the word definition here should be interpreted as squishy and non-strict.
In most of the world that speaks a more British English, terms like city and town have pretty specific definitions. That’s just not the case in the US. Language is funny, huh?