A lot of this is going to be subjective and depend on your personal frame of reference, as well as local laws and customs that can vary a lot around the country

In general, in normal casual conversation, most Americans are going to refer to a municipality as a “town” unless they’re in a big city. Legally, that municipality might be considered a city, town, township, borough, home rule municipality, village, etc. but unless it’s a big city we’re probably going to refer to it as a town most of the time

There’s also, in some areas, unincorporated communities that don’t have an actual municipal government, but if there’s a relatively dense area, we might go ahead and refer to that area as a town.

Some parts of the US do have some sort of legal definition for “village,” in others it might be used informally to refer to a small “quaint” town, or part of the town.

There’s also the distinction of, for example, being “in a town” vs “in town” or “downtown”

Most of us who don’t live in a big city would say that we live in a town, meaning the municipality we live in. Somewhat less of us live “in town” meaning something more like the denser, more “urban” parts of town, probably resembling what you think of as a village, and “downtown” would refer to something like the area around the main street or main commercial area where you might find stores, restaurants, bars, etc.

So a “rural town” is basically any sort of town in a rural area. I’m not sure if there’s any sort of a legal definition for a rural town, but in general I’d say that if a town is surrounded by woods and/or farmland and you can’t trace an unbroken path of suburban sprawl from it back to a major city it’s rural.

Some of those rural towns can actually be fairly big and urbanized, but they’re otherwise in a rural area in their own little bubble so we’d still consider it to be a rural town.

As far as town vs “small town” that’s kind of subjective.

The town I grew up in is often referred to as a small town, largely because it’s physically pretty small, almost exactly 1 square mile, but that 1 mile is pretty densely populated, I think the population is around 9-10k people currently, it’s just a couple miles outside of the nearest major city, and pretty well-urbanized itself, connected to several major highways, was once a big manufacturing town but is now pretty gentrified, with a solid handful of 10+ floor office buildings. People from more rural areas probably wouldn’t agree that it’s a “small town” but people from a bit city probably would think so, and for those of us “townies” whose families have lived here for a few generations still feel like it has a small town feel, even if the newer transplants don’t all share that feeling.

The town I currently live in isn’t quite rural, but it’s getting there. I’m towards the edge of the suburbs now, maybe even into the exurbs. The town is physically much larger, but only has about half the population. That small, less dense population makes it still feel kind of small-towny.

Also worth noting, my town doesn’t really have any sort of a “downtown” area, no real main street to go walking around or anything. We have a few businesses and stores and such roughly clustered in the same area, but it’s not a cohesive thing that feels like a “town” or what you might recognize as a “village.” I would normally may this, but if I said I was going “into town” for something, most people around me would probably understand that I’m going to one of our neighboring towns that are a bit more built-up

So some combination of physical size, population, population density, and a curtain je ne sais quoi are what makes a town a small town.