The game industry technical definition of MMO is narrow subset of games where the world is persistent and hosts large amount of players at same time. However the psychological definition is more broad:

A MMO(massive multiplayer online) allows players to form connections with large amounts of people using the game social features.
Under the psychological definition, most multiplayer games will be considered "massive" nowadays, even if the game world is instanced and small(e.g. Diablo2). So what is the key difference?
The key difference is that MMO games are enabling large-scale social structures(binding groups of people with common interests) to form and interact with each other - not their technical world-hosting capability. i.e. League of Legends is psychologically a MMO, but not in the technical sense.