both are Surgeon fish so possibly they are fighting and the yellow is just getting the brunt of it. the fins being ripped is probably caused by that sharp spike on both sides of their tails. hense why they are called surgeon fish
are they fighting alot. what size tank and how much rock,
you could try turning lights off for a week even put a blanket over tank to keep all light out. only turn lights on to feed and when you can watch them. at first sign of a fight. shut lights back off.
recently saw a yellow Tang at a LFS that was so beat up by a purple his owner returned him. pretty much finless. they can do alot of damage to each other if left to their own.