Actually, not at all...
A few differences.
MFC = You pick a job and just fight melee-style, free for all.
Warfare = Your goal is to assinate the general/king, if you picked general, you stay in the castle's room and shoot regenerating ammo down for the recruits from a higher level at the ammo room, if you picked any of the others, you fight on the battleground and try to kill the enemie king (and going through a obstacle parcour sometimes, depends on the level) or defend your own castle/king.

And about Quest, I know that the description might fit with a lot of single player levels, but play LoC and you'll see it's different from the others, and that's a typical 'Quest' level.