I don't think plakats are the same as king bettas. Plakats are just short fin bettas. This type usually used by people to fight (no one here will do that of course). They short fin, faster and much stronger than the other type with higher immune system usually. King betta or giant betta can grow twice the size of a normal betta. A normal one usually stay around 1.5-2.5 inches, where a king or giant betta could grow up to 4 inches.
Yes, I have seen other type of giants as well, but only in picture and not in person of course.
Big/elephant ear betta are just bettas with big pectoral fins. And again, usually i see them in plakat form
but recently i bought a halfmoon elephant ear
I've seen king betta at petco, and i think they only carry plakat type since they the most common form of giant betta