Matchmaking = You can actively search for other players, get EXP, get rank, etc. Custom Games = You can't.
Basicly, Matchmaking contains game types that are regulated by Bungie. They allow you to earn EXP, gain rank and play with random people quickly if you don't have friends to play with. Custom is only for friends and friends of friends. You have complete control over the games and maps. You don't gain EXP or rank and you have to know people in order to get people to play with.
Custom Game = Teh Funnest! Matchmaking = The dying need of exp. Matchmaking really gets boring after a while, so now I just stick to Forging and Cutsom Games!
custom games r regulated by the leader and no one else decides, mm the party itself choses by vetoing.
I stick to custom and forge too (especially forge), but it does suck, because whoever the leader is has complete control over the party. They can boot you for no reason whatsoever and wait for an hour to start the game just to tick you off.
custom=fun with friends matchmaking=fun with strangers thats y some younger kids arent alowed to have mics talking to strangers=danger