In the “traditional” sense, most people consider an RPG game to be a Pen & Paper RPG in the vane of Dungeons & Dragons, Pathfinder, 13th Age, Savage Worlds, etc. The game is played more in your imagination and off your character sheet than it is on any kind of board. Talk to any boardgamer and mention “RPG” and that’s generally what comes to mind. The “boards” are usually ‘battlemats’ for working out position during combat and the like, but much of the game is not played on any type of board.
Having said that there’s quite a few boardgames that are what some people call “RPG-Light”. They’re played on a board, feature lots of bits, and include some type of character progression for the play session. They’re usually much more theme-heavy than typical board games, but not as much as full blown RPGs and are generally self-contained. Unlike P&P RPGs these don’t typically have any kind of character persistence beyond their play session (and the game can be won/lost in a few hours), so you start over every time. Games like Mage Knight, Runebound, Talisman, etc. could fall under this category.
ACGs (Adventure Card Games) probably fall somewhere in the middle.
My game falls under the “RPG-Light” category. It started out as a massive houserule for Return of the Heroes, but it got too the point I was changing so much that I just decided to start from scratch. I’ve re-used many of the mechanics and conventions in that game (the counters for example follow the same layout and have similar symbols meaning the same things, I maintained the 16-tile geomorphic board format, etc.), but with all custom artwork, overhauled dice mechanics (converting all the game mechanics from d6-based to d12-based), and a new story-heavy theme. There is character progression in the game (I’ve also added a basic skill system), but like most RPG-Light boardgames there is no persistence between play sessions. I’m also designing it primarily for solo play.