I think possibly the confusion lies in which registry we are talking about. The only pattern term used in registration by AMHA and AMHR is Pinto. Tobiano, Frame (LWO), Sabinio, and Splash are all genetic terms that describe which type of Pinto, but are not used on registration forms. Medicine Hat, War Bonnet, Morrocan, and others are descriptive terms, but are not the result of one specific gene, but a combination of different genes. All Medicine Hats would not necessarily have the same genetic makeup.
I will admit to having no knowledge of the terminology used by the Paint Horse Association, but do not accept them as the authority on genetics or patterns.