How about this as a definition.
imagine that as the game is released, 10% of the universe is known, 90% unknown.
if you play Single player off line then you get to explore the 90% all by yourself
if you play single player online then any of the 90% that you explore gets uploaded for everyone else to know about and vice versa, but you are still alone in the universe apart from the NPCs
if you play MMO, you play in a group of players. That group might be the ALL group or a smaller group that you define or join, such as the "Over 40's who do not want to be griefed"
and you can only change mode or groups at a space station
imagine that as the game is released, 10% of the universe is known, 90% unknown.
if you play Single player off line then you get to explore the 90% all by yourself
if you play single player online then any of the 90% that you explore gets uploaded for everyone else to know about and vice versa, but you are still alone in the universe apart from the NPCs
if you play MMO, you play in a group of players. That group might be the ALL group or a smaller group that you define or join, such as the "Over 40's who do not want to be griefed"
and you can only change mode or groups at a space station