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.