Eh, I understand using the distinction just to make things easier.
I mean yes, Persona 4 and Skyrim are both RPG games, but due to the differing mechanics and art styles, I understand why people would prefer to differentiate them a bit more than that.
What makes it so difficult is that for the most part, there seem to be two differing definitions of what "is" or "isn't" a JRPG. Some people try to use it as a term meaning the genre, and some use it to just say "It's an RPG...from Japan." and neither of those are really wrong, and they don't conflict with one another.
For instance, I once got flamed pretty badly on GameFAQs because I referred to Fire Emblem Awakening as a JRPG. The retaliation was basically "It's not a JRPG, it's an SRPG!" followed by random insults and expletives that aren't important right now.
And yes, Fire Emblem is an SRPG because...well again, people come to define a genre by its mechanics. It's an RPG that uses grid based combat, so it must be an SRPG, right? But...by saying "It's not a JRPG" are you saying Fire Emblem is...not Japanese?
It's weird and its messy, and I don't really think there is a right or wrong answer on this subject.
For me, whenever I see anyone use the terms, I usually just get what they're talking about, and it's just something where I don't feel like getting into the semantics of it.
When someone says WRPG, I can assume they usually mean a more free roaming game with real time combat, like Skyrim
And when someone says JRPG I assume they mean a random battle, turn based, etc. etc. type dealy like Shin Megami Tensei IV.
Then I just check what game they're actually talking about and go "Oh okay, that's why they said that." regardless of whether or not it fits those preconceived notions.