After or during certain moves, you can use an additional command input in order to perform another move. This is an add-on move.
If there are two or more different moves (or routes) that this additional input can perform, then the add-on moves can be called derived moves.
For the most part, if you perform it, you will make yourself more open, so it tends to go hand-in-hand with hit confirmation; if you do not hit the first time, it is usually to your advantage to stop instead of making the situation potentially worse (but sometimes it helps rushdown).
The advantages of add-on portions include extra damage, as well as the possibility of forced knockdown (and yet, there is the occasional possibility that another move is much better for following up, so you should not use add-on moves as a crutch).
Finally, some add-on moves will only happen if the initial move successfully hits.