Co-op missions are missions where you have to have a certain number of players in the team to finish the mission, you need to cooperate with each other, too.
"Party" missions are always on time.
You need 4 people to do "Her Secret Mission" in the GUARDIANS Ohtoku Branch.
Same goes for Bruces Dungeon located in the GUARDIANS Moatoob Branch.
http://psu.amesani.org/stuff/mission/list.php?type=2
As for other missions.. (which are "Free" going from Amesani)
You need at least 2 people to finish the mission Cost of Research which you can do backwards from the Kugo: Hot Springs.
And I think you need a certain number to do Stolen Weapons in Moatoob, too.
Well, that's what I know of so far, dunno about other missions.
Well, basically, they are missions you can only finish/complete with at least 2 people or more.
Else I don't think there are other big differences..~