If you would have read my post more carefully you would have seen that I'm not speaking of official terms. I'm referring to what it means when people, specifically gamers, talk about RPG's in a casual conversation or exchange, and you know that gamers do use those terms in the context in which I spoke.s69-5 said:
Since you're so found of formalities and technicalities, Dark Souls is actually the spiritual successor of Demon Souls which is the spiritual successor of King's Field, and since they are "spiritual successors" they are far less bound to stick closely to the original game's formula. And for the record I'm well aware of how the unofficial roles of so-called JRPG's vs WJRPG's has flipped over the course of the 90's and new millenium. Yes, JRPG's were originally the more action based ones where as western ones were more rule-based, mainly because of the usage of a controller for JRPG's whereas their western counterparts were played primarily on computers with a keyboard and mouse.
Are they official gaming terms? No, but they are used by enough people to know and acknowledge that when someone says Japanese or western RPG they're (correctly or incorrectly) describing a certain cultural style of game, not it's origin. If we go by origin the vast majority of games are Japanese but that description blindly leaves out cultural influence.
Yes, those are the true categories of RPG's that you listed. Just don't ignore the slang terms, or more importantly be able to discern when someone is using them as slang since they also mean something to lots of gamers out there.