The definition of massive here is an open question. For the sake of the term though a massively multiplayer generally is
persistent massively
multiplayer. Where persistent will be defined as something lasting longer than say a day, to months or years at a time, in which the state of the world is shared, and almost any one can login and logout of the game at any time with their character or empire continuing to exist, and some times change during their absence.
Given this free presence a massively multiplayer game or MMP can have a thousand players in the database, but only one on at a time (
however unlikely this is). Also a MMP game could exist across multiple subservers which would support only a part of the total world and be linked together allowing effects and players or actions to transfer between the subservers.
I think the confusion here is over the use of persistent. It does not necessarily mean that the character (in the case of a
MMORPG) continues to exist *in* the world, but that the world continues, and the characters continue (at least normally) to exist in the
database. On the other hand there are MMP strategy games, the majority of which to my knowledge are web based (such as
Planetarion) have the empire continue to trudge on to success, or more likely failure, even in the absence of their leader.