I think a semi-detached is a duplex, but the latter term is more broad, covering also two-story apartment buildings and such: https://en.wikipedia.org/wiki/Duplex_(building)

Building with two separate housing units. In most of the US, probably similar to what you call a "semi-detached" or Germans call "Doppelhaushälfte" (units are next to each other, sharing a wall in the middle), but especially in the Northeast, sometimes a larger old house split by floors (ground floor and basement as one unit, second floor and attic as another unit, with some sort of separate entrance to reduce disturbance of first unit residents)

Two end of terrace houses next to each other. If you want a standard "semi-detached" house in the US it's normally called a townhouse (or similar).

> So what is a duplex?

A single property (usually a single building) consisting of exactly 2 housing units.

> I guess "semi-detached" would be closest but not sure?

Semi-detached is similar, but AFAIK usually refers to separate properties sharing a wall not two housing units on one property. There appear to be regional variations in both terms, though.

Coming from the East Coast of the U.S. I always called these houses twins. One building with two housing units side by side, usually mirror images of each other. We would refer to a building with two housing units above and below each other as a duplex.

It's a home that's been divided into 2 homes, usually with paper thin walls. At least that's been my experience in the USA.