I'm gonna toss a third term in here: premise. A lot of MMOs have a great premise, but fail to execute too much on telling a story. Wildstar comes to mind. It had (some) lore, but had very little story to match the game. Why you were there and what you were doing was limited to the tutorial on the spaceship, and then you were unleashed into the wilds to go exploring. Great premise of planetary settlers with opposing factions. Mediocre lore limited entirely to in-game quest assets and a basic website at launch and not much else. Very, very, very little story.

Hence, Wildstar was not a story driven MMO. It was a sandbox MMO that had a cool premise and some basic background lore. "Here's your lego set, here's the rules, now go play!"