This might make me a total noob but  i think co op is when you do a story in a game with a different players.whereas online multiplayer is when you do different modes but not the story line.

for e.g. halo 3 has 4 player co op but online multiplayer it has up to 16 players. is there a different between multiplayer and co op 

Coop is when a group of 2 or more players work together to accomplish objectives, whether it be by working through the main story or special coop missions.

'Multiplayer' usually means players trying to beat other players (by killing them or beating them in a game, or whatever the rules are).

Any game with multiple people is "multiplayer."

Within "multiplayer" there's co-op and competitive play.

Co-op doesn't have be a story mode with multiple people, but that generally works the best.

and i'll add to BenKenobi88 definition that you can do it online or offline

I guess you could consider WoW a co-op game since you raid in groups...
Though for me Co-op refers more to doing the same thing sitting next to your friends :p (but that is just me)

Co-op is often "playing the same game and sharing points," but there's definitely games that have you doing different things and working together and whatnot.

Such as Guitar Hero, you don't both play guitar, you play guitar and bass.

double post, site is being stupid.

Co-Op is when 2 or more players co-operate to play against computer opponents in a story based missions. Online Co-Op is when 2 or more people co-operate online to play against computer opponents in a story based missions.
Not all online multiplayer games are not co-op and not all co-op games are online.
Usually offline co-op is implemented splitscreen (Halo1,2,3, Darkwatch(PS2) etc .. most fps and third person action games implemnt co-op as split screen, or shared screen Marvel Ultimate Alliance, Baldurs Gate Dark Alliance, Champions Of Norrath, Double Dragon 1,2,3, Streets Of Rage 1,2,3 etc.. Brawlers, Beat Em Up and RPG's are usually shared screen.
It is relatively simple to implement local splitscreen and same screen co-op. Online co-op requires tighter scripting and programming than what most studios can devote.