Uhm, your character is defined by their stats, skills (theoreticaly speechcraft) and character traits (prejudice, fears, moralcodex etc), culture, profession.
Personality is the spice on the dish called character, but even that is influenced by attributes like courage, intelligence, charisma, skills like etiquette, being a cliché dwarf (T_T)...
It's less confusing if you know the history of where tabletop role-playing came from.
Tabletop wargaming involved recreating historical battles, but the leader of one group in Minnesota was starting to get a little bored of it. He decided to spice things up by including additional characters: instead of just two generals battling each other, he added characters like a town mayor and a university chancellor, each assigned to a player.
These characters had no armies.Their purpose was to make character-driven decisions while interacting with each other. They could even go in another room to make private deals, so no one knew who might betray who. Playing a role like this became known as "role-playing." This was essentially the first role-playing game.
A guy named Dave Arneson was in that group. He decided to lead a similar campaign of roles, but he'd also been reading Lord Of The Rings. Instead of a historical military setting, he decided to set it in a fantasy world. He called this campaign Blackmoor. However, some players were frustrated with the lack of structure of early Blackmoor. Arneson was more into the storytelling potential of having individuals act out characters within an author's story, but some players wanted proper game mechanics they could fall back on. Arneson and his group decided to try adapting Gary Gygax's Chainmail rules to individual players rather than armies.
That worked out okay for awhile, but eventually Arneson approached Gygax directly about creating a proper rule set. This collaboration became Dungeons & Dragons.
Character-building with stats was not role-playing. Character-building in terms of character and personality was role-playing, and the stats were there as structure for the battles.
If you reduce the term RPG for games to personality based choices there's like nothing left as RPG-game since most games that allow different dialog don't lock you in (in a personality) as far as I remember/played right now (IS there a game that recognizes shizophrenic choices?).
Games with character interaction like Mass Effect (which hail back to much earlier games like Star Control 2 and the even earlier Starflight) are the closest we have right now. You could even say Telltale's The Walking Dead is closer to true roleplaying than stat-driven games like Wizardry, Ultima, and Dragon's Quest and the games it inspired. But technology is still too limited to really give players the full freedom of a proper DM-and-player role-playing experience.
