for me :
• You win exp and become stronger by killing enemies -> it's a RPG (Like Castlevania 2D (Plateform RPG), Seiken densetsu (being Action RPG as it's not turned base))
• Enemies doesn't give exp, you can skip their battles because you become stronger only when you find upgrade items -> it's an action/adventure game. (like Zelda, Metroid, or Castlevania 3D)
• Sometime it's in-between, You don't directly get exp by killing enemies but your equipment or skill level up.
The limit between RPG and not RPG is thin for me in this case, just the game feeling determine it.
Though, there are also RPG without exp or hitpoint at all : Text-RPG like Suikogaiden or Radical dreamers. but it's more Text adventure games than RPG.
I don't consider "Playing a Role" as being a RPG, because EVERY games in the world where you move characters you are playing their roles, but they are not forcefully a j-RPG.
And I don't consider Tales of and Star Ocean as Action-RPG, but as traditional J-RPG. It's not because it's not turn based that it's action RPG. For me, A-RPG is when you don't have specific Battle phase, when you do your actions on the enemies directly on the traveling field (like Secret of Mana).
On an old thread I participated, we argued about each other's opinion about what is really a RPG, and everyone has his own view.
He think Pandora tower is not, for you it is. That's all. Just a point of view about what you consider being a RPG. for me, "Exp winning" is the key.