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).
Here are some descriptions and photos of what most small towns look like: https://www.onlyinyourstate.com/trip-ideas/washington/slow-paced-towns-in-wa
A really small town is like what you’re calling a village. I think most people outside the US think that rural is closer to urban areas than it usually is. It typically starts a half hour outside a major city and then can be 7-10 hours to the next major city depending on what state you’re in. The upper east coast is probably closer to Europe. Rural encompasses a huge swath of the US land, and most are very isolated physically and mentally.
Here is a map showing the population densities by county: https://irjci.blogspot.com/2020/08/census-bureau-to-end-counting-efforts.html