All is correct Meade except for the point about King's and their caudals. King's are larger Betta fish, often referred to on AquaBid and here as Giant's, PetCo just named them Kings to make it more fancy. It has nothing to do with their fins except that you can have a Giant PK where fins are shorter or you can have a long finned Giant like the last boy where his fins are normally sized, he's just huge! Often on AquaBid the boy's are very young and their fins still have a LOT of growing to do so that is why they look so short in the pictures.
So to reiterate:
: 2 rayed CT that the ray's a close and side by side like the first boy Meade posted. Double Ray's generally go straight out unlike V Rays
Double Double Ray
, also known as Four rayed CT is just that; 4 rays.
: similar to Double ray where it is a 2 rayed fish but they ray's make a V shape, similar to Cross ray but the ray's do not cross. This girl is a V Ray, it's like the in between of Double Ray and Cross Ray
: the ray's cross each other like Meade's last boy.
: Where the ray's don't particularly follow a specific pattern like this guy, they are just that; random!
: PK's or Plakat's are short finned Bettas so they are short finned bettas with crowntail finnage like this boy: