A "King" betta is a giant PK. They breed them to be larger than the normal sized PK. I don't think we're really sure how they get them to be that big, but maybe one of the breeders can help describe it to you. Yes, they are both bettas and yes, they breathe air.
Kings need bigger tanks (5Gs or more). They also need to get fed a little more because they're bigger. They're short finned bettas so they zoom all around and can jump very easily so if you get one, make sure to secure the hood and cover up all the holes. My King jumped out and died. :( It was such a small hole that I never thought he'd get out, but he did.
I am thinking of getting just one "king" betta for my 20 gallon tank (he will be a king LOl ...anyway i have a cover w/ a light ,but i guess bettas dont want a light ? and im not sure how secure the cover is ? my tank is 20 gallon long...maybe i shouldnt fill the water too high because of the jumping thing...how far can they jump ? maybe i should get a screen top instead ?
You should leave a couple inches free from the top. I'm sure he would love being in the 20G. I'm not sure how high or far they can jump, but they can jump. Bettas need a day/night schedule like we do. I put my tank lights on for 8 hours at night and shut them off during the day.