it is a lot of times a betta that has the CT trait , but doesnt have the fully formed CT , the rays arent fully extended. There is also the Super delta and Double tail which are also cool.
BF usually stands for butterfly. When the dorsal, anal and caudal fin are divided into two colors... almost proportionately. When one half is one color and the other half is another color.
I've had lots of bettas in the past, but just the veiltails from the petstore -- up till a few weeks ago, I had no idea there were so many varieties out there! I'm quickly getting addicted, haha.