Player versus Environment

Player versus Player

Players might be ale to fight each other, might be able to steal other players items, but it is not the goals of the game. (some games have duels, fights against each other without consequences.)
The player plays the game with set goals. The players can team up to fight 'bosses', or build together.

Players are able to fight each other, steal each others ingame items. Depending on the rules there are several ways to use a death mechanic. "Permanent Death", similar to iron man mode or respawning (with or without penalties)
Players are less likely to team up as there is always a incentive to kill your fellow player.
A good PvP game is Eve-Online

Playing the game to continue indefinetly. There is no real winning point, but there are goals to follow. It is important to have short term plans and long term plans and the long term plans may change.

The game has a finite gameloop, like chess, checkers, football. There are certain conditions that define a victory. When the conditions are met it is a victory. A victory means that the gameloop is done and a new loop has to start.