LOL!! I used to think that they all had to be coloured......
APHA - American Paint Horse Association. They were originally a splinter-group from AQHA when AQHA tightened up their regulations about colours and markings.
Biggest problem with APHA in my opinion is that they allow solid horses into it because numpties keep breeding solid coloured Paints so because they are still offspring from fully registered parents they have to be allowed into the Stud Registry.
Perhaps you are thinking of Pinto? That is not a breed - just colour.