When you breed bettas, the genetics within both the parents and the offspring are either recessive or dominant. Some of the characteristics of each gene would show in the offspring, but it wouldn't be a direct combination of both.
For example, if you breed a plakat with a halfmoon, you wouldn't get a betta with a long anal fin and dorsal fin, and a plakat caudal. You'd get whichever is dominant- in this case, the long fins would be dominant over the entire fish, so you would get mostly long fin halfmoon bettas.
Just the same as when you have a deck of cards and you shuffle them- you don't just get one big card with all the numbers shuffled onto it, but rather you get "layers" of cards, and only the one that is on the top of the deck will you see.
If you were to breed a female plakat and a male veil tail, you would get all veil tails because it is a dominant trait. However, if you were to take one of the offspring and breed it back to a plakat, you might get a few plakats out of it because it is a plakat genotype.
It's confusing at first, I know, but study your toosh off and it'll all make sense eventually. xD