This is something that has been bugging me. A lot of people on this forum seem to think that the term co-op (cooperative) is synomymous/interchangable for the term multiplayer.
This is not the case. Co-op is simply one type of multiplayer, in which the two (or more) players play cooperatively/collaboratively. In other words, the players are not competing against one another.
Multiplayer games in which two or more players are competing against each other in some way (e.g., fighting against each other, killing each other, playing a sport against each other) are NOT co-op games. They are simply multiplayer games.
That being said, most games that have multiplayer portions contain multiplayer portions that are not co-op.
End public service announcement.