"apart-hotel" isn't really something that exists in the US. And I had no idea it was a searchable term in some online booking tools.
Somebody mentioned extended-stay hotels elsewhere as the closest analog in the US, but they tend to be focused on business travelers, and not always located in tourist areas. For example, there are a ton of extended-stay hotels near my office, but that's 30 miles outside Washington DC in the heart of the northern VA internet/tech zone (AWS, Google, the remnants of AOL, etc).
Edit - I'm looking at Hotels.com now, searching Inverness UK from the US site. "apart-hotel" is not an option under "Accommodation Type". Apartment is a distinct type from hotel, and it appears to be a mix of what you describe (bocks of apartments managed for vacation lets) and individual apartments (Airbnb-style).
Sometimes I stay at "apart'hotels" in Europe. At least at the chain I've used a number of times, it's really just a hotel with 1.) Some cooking facilities like an extended stay place in the US and 2.) Cleaning is just weekly. They also tend not to have features like bars and gyms that many hotels do. But, really, at least for my uses it's pretty much a hotel with a 24-hour front desk.
If it says "we have a great atmosphere, and go clubbing every night" it's a party hostel.
If it says "we have family and dorm rooms, kitchens and car parking" it's probably for families or school trips.
There are also hostels used by people who are essentially homeless, though I've never seen one advertised. I knew someone who volunteered at one.
On hotels.com, what you're looking for is described as an "apart-hotel".