Fin rot is a condition that, overtime, literally rots the tail. It is caused by extensive periods in dirty water, either on its own or after a fight or chewing. But the edges are black or red and look like they're slowly deteriorating.
When a betta noms its tail, little chunks are taken out. Giving it a ragged, split look.
Clean water and indian almond leaves should clear up a chewed tail. To help the condition, add more plants or toys to the tank to give them something to do. A lot of the time it is caused by boredom, stress. Oftentimes a betta with a heavy tail (rosetail, halfmoons etc) will bite to lighten the load.
If it is, in fact, fin rot I would suggest a small dose of aquarium salt. 1tsp per gallon. For a MAXIMUM of 10 days.