Interesting thread, especially about the duplexes; I've often wondered what constituted one of those. I had in my head some kind of arrangement like our semi-detached houses.
I live in a large Edwardian house (UK, so about 100 years old I guess) which while originally would have been one dwelling for probably a well-off person/family, has later been divided into four flats. Two on the ground floor and two on the first floor. It has a shared front door to the street and a communal hallway, with the internal doors to flats A&B on the ground floor then the doors to flats C&D on the first at the top of the stairs. This kind of place is very common here especially in cities. What would this kind of building be called in the US? I get the feeling they wouldn't be "apartments", because they're not in a block. When I think "apartment block" I think like the place they lived in Friends. Purpose-built, in other words, rather than a house converted into two or more dwellings. We just call them 'flats'.
There are different kinds of flats though - the one I live in are 'converted flats', often referred to in sales particulars as 'ground floor conversion' or 'first floor conversion' etc. There are also purpose built flats in developments or tower blocks. 'Apartment' hasn't really made it over here, except to describe very high end luxury flats.
I've lived in a large, old house converted to apartments. At least in my area, there's no real specific term for that type of building. We just called it a "house converted to apartments." And the individual units were called apartments, because in general in the US, "apartment" is used for any individual dwelling unit contained within a larger building with multiple dwelling units. (That's a dwelling unit that is rented. The same dwelling unit in a larger building where the unit is owned and not rented is usually called a condo.)
In the New England area, the only "apartments" that don't always get called apartments would be two and three family homes. But a house converted to three apartments wouldn't be called a three family home, but a house converted to apartments.
I think it is because the two and three family homes tend to have an entire floor for each unit, and there is more space and they feel more like a house than an apartment. In my area, the two and three family homes tend to be older, built before 1930 or 1940, so they have large kitchens, pantries, laundry rooms, separate living and dining rooms, built-in china closets, things like that. While most apartments tend to have combined living/dining rooms with an open kitchen stuck in a corner of the room, few to no built-ins, no laundry hook-ups and less storage space overall.
To further muddy the waters, you wouldn't call a house converted to apartments an "apartment building." That is used for a building that was specifically designed to have multiple apartments in it.
I've also lived in an "apartment complex" that was a series of small buildings, each building having 4 apartments in it.