There is a Betta which has been developed that has a spot/cap of different colour on its head. So the main body colour is say blue and the spot is black. This spot of colour varies in size, but is normally about 5mm diameter.
As mentioned, there are mutations which are harmless and do not affect the bettas health like colours and fin shape. These do not really cause any internal issues. Where as, Doubletails have shorter bodies. This shortening of the body has caused, as it has in other fish species, swim bladder problems. The swim bladder organ extends nearly to the tail, and in short bodied fish it is squashed. From the double tail, some people have gone on to create what is refered to as "short-bodied bettas". These SB's have kept the short body, whilst losing the doubletail. There are inherent problems with these fish regarding swim bladder issues, they do not live as long, and other problems include the lack of dorsal fin.
My own belief about breeders of such mutations like the short-bodied are that they are either oblivious to the problems or just dont care!