Well, the most strict definition of an RPG is something that takes root in classic D&D. That's where the phrase comes from, and how it all started. Back then, the main focus of D&D was the role playing, because your character interactions were every bit as important to the game's success as the Dungeon Master's.
As a video game genre, it has vastly strayed. It started off as dungeon crawlers. I'm sure you've seen the old games where you go through the vastly similar hallways one square at a time. However, due to the lack of technology, story was not very prevalent like it should be in a Role Playing setting. I'm sure games like Ultima allowed plenty of kids to imagine their own adventures, but the main focus of the game was exploration, which included often drawing your own maps, and a lot of tedious fighting. Most gamers of this generation will never go through the pain of thinking, "Oh god, what was the name of that really awesome fire spell again? Bloozankin? Blasterinin? F*** it, I'll just attack with my fists."
There's some debate over whether text adventures are the true RPG's, as a good one is the closest you can get to D&D, the base, but text adventures haven't been quite as prevalent in gaming.
Naturally, dungeon crawlers, which were the very first interpretation of trying to bring D&D to a game, did not really appeal to anything even near considered a casual gamer. That's when Japan came in with their wonderful creation of a game called Dragon Quest. That was the start of the JRPG series, which was much more popular. The popularity came from the simple story, the streamlined menus, the sense of purpose, and actual character interaction. Not much mind you, but more than had been seen before. But games like Dragon Quest and Final Fantasy were directly made in order to counter the elitism needed to succeed in games like Ultima. In fact, a much more accurate term for JRPGs would be LRPG, standing for Light Role Playing Game. That's what it was, a D&D style adventure with a majority of the choice and customization cut out for the sake of experiencing a definite experience that everyone can enjoy.
So, for the majority of gamers, the choice between RPG and LRPG was easy to make. It was a much easier debate than the WRPG vs. JRPG debate we have currently, simply because the technical capacity meant all of the RPGs were f***ing difficult and only catered to people with time. As Japan, the basic monolith of gaming, kept producing, LRPGs were the main focus in the genre.
As time went on though, the inclusion of MMORPGs and various WRPGs started expanding the focus again. Instead of having a strict streamlined approach so everyone can enjoy the same game, they decided to go back to the root and open it up so everyone has their own experiences. I think, looking at games like Elder Scrolls, that it is surprising to see just how much technical capacity can change the reception of a genre. WRPGs, which are strikingly closer to the actual definition of RPG than any other form, have been picking up a lot of steam as of late.
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"I can already feel my Dumey Lust kicking in." -MistBiomeZ