A derived move is a kind of add-on move. It is a derived move instead of just an add-on when you have two or more derivations from the originating move.
Similarly to add-on moves, if you go along far enough or only so far, you will often increase how open you are; however, depending on the move, you will often have an actual choice between options, like between an overhead or low hit, so if the previous move has been blocked, the input might just be worth it.
For example, Kyō from KOF ’96 onwards has two similar flaming punches for + A and + C. However, the weaker punch has two derived moves, whereas the stronger punch has one add-on move. The former has multiple routes to take; the latter has one.