So what's the correct term for "a cheap hotel, usually without a minibar in the room"? Because that's what we call a "hostel" over where I live, and I assume in the rest of Europe.
Motel. They're usually what you'd expect from the lowest end of hotels, and (at least around here) a great many of them are left over from the '50s through the '70s—the pre-interstate era, where driving to visit somewhere several hours away usually meant stopping in some little town overnight.
I haven't personally stayed in one, because I have enough money that I'd never have to, but the impression I have is that one would contain a bed, a desk, a chair, a not-entirely-spotless bathroom, and not much else.
That's certainly the image that the "motel" term conjures up. TBH, I'm not sure how broadly the term is used any longer. There are certainly more modern hotels/motels, many of them big chains, that are designed around people driving to them so you can usually park near your room.
The quality varies from pretty tired and not so clean, as you say, to--if not upscale exactly--to comfortable, modern, and clean.
Oh, yes; there are certainly many chains like Travelodge and Motel 6 that fit the category of "motel" but are more modern and clean.
However, I can quite assure you that here in rural Upstate New York (and, indeed, even in some of the less-well-off sections of the cities), there are still a great many motels that date to the era I mentioned—very visibly so. (This is why I qualified my statement with "at least around here".)
I have actually stayed in Travelodges a couple of times, and while they were modern, I wouldn't really describe them as "comfortable" (the beds were like tandem canoes) or "clean", at least not universally so.
I'm thinking more things like Comfort Inns or the lower-end Marriott brands. I'd put Travelodge and Motel 6 pretty near the bottom of the national chains. I had the misfortune to have to stay in a Travelodge last year because of a last minute trip.
But, yes, there are also still quite a few non-chains or small chains that aren't... great.