Discipline: Being as gentle as possible, but as firm as necessary.
Abuse: The minute you cross that line.
I have seen people welt their horse. Some situations, I would call it abuse. Others, I feel it may have been justified (VERY dangerous/rude behaviour, there was a progression of the aids, warning, and every chance for the horse to answer the question the 'right' way and make it stop). The horse understood and had a chance, they just said "make me" and the person said "Okay, I will". Discipline was applied, and the rider asked "Do you want to rethink that answer?" the horse says "No. Make me" and the rider said "Okay". And it went on like that until the horse said "I changed my mind, I'll behave" and the rider said "Okay, good boy".
I think a lot of what qualifies as abuse depends upon the manner/attitude of which the action is applied, as opposed to the action itself.