I can give you a general idea, saying that the ones above kinda suck. But yeah, there both kinda right. Um, allright. First of all, if you go to www.bungie.net and search ranking system they spill all the details of who gets what amout of points, and its really complicated, like, im in calc and its more complicated than i wana deal with. Ok.. First... You wanted to know about EXP.
As far as i know, EXP is not really a rank, its there more to show how much you have played. You get 1 point from winning a team game or 2 points from winning in a free for all game. EXP goes up over social (unranked) and ranked matches. So, no matter what game your in online, as long as its not a custom game, you get EXP from winning it. This goes up from private up to higher ranks. As you increase your exp there are rank lvl requirements to reach higher ranks. So, after a certian amout of exp, you need to be a lvl 10 or higher in ANY matchmaking playlist, or have reached that level before. (if you get up to a 45 and then drop down to a 20, it will say your highest level is 45). So you can skip ranks, maybe you need 200 exp with no rank to get this exp rank, but if your lvl 10, you only need 100exp to get a higher rank. Its hard to explain, but check out the bungie website for exact numbers.
As for matchmaking, its more fun. The numerical rank that you have differs in each playlist. You can be a 33 in Team slayer and still be a 1 in lone wolfs. This rank goes up based off of a version of "Trueskill" Matchmaking system. Its like this. You have 2 teams of 4 people. ok? ok! so your on the loosing team, but you did the best on your team, so your technically in 5th place! So, you lose points for being 5th, but you lose less points than the people in 6th, 7th, and 8th. Also, if your on the winning team and as stated before, the other team outranks you, you will gain MORE than average points. There is nothing saying "if you win 2 games in a row you will rank up, or if you get mvp you will rank up". Nothing like that. Its all based off of numbers. So out of the 8 people that played, 1st place gets most points, 2nd gets a little less points, 3rd gets even less, 4th gets the least points. From 5th on down, 5th loses the least amount of points, 6th loses more than 5th, 7th loses more than 6th, and 8th loses more than 7th. Hope this kinda makes sense.... Once again tho, check out bungie.net for the full detail! Hope to see you on live sometime! Gamertag: r0bdawg11