I actually enjoy playing NTR games - at least the ones I've played. To be fair though, the player is usually in the role of stealing other people's girls.
I highly recommend this one - it's hands down one of the best I've ever, ever played.
The Hero's Party Must Fall - after all, it's way more fun when you cuck someone else.
You're right to a degree.
NTR is the genre.
The two you mentioned are sub categories. In fact, that's why I chose both of those sub categories as examples to explain what NTR is (and isn't).
As you can see both have the letters NTR in their words, to further explain where they originated from.
Netorare , Netori = a type of N.T.R.
Sort of how apples and oranges belong to the fruits category.