I noticed that there is a "2v2 team" (3v3 team, 4v4 team) section in the "leagues and ladders -> friends" in addition to "2v2 random". It is my understanding that what I've been playing is "2v2 random". What is that "2v2 team" ladder?
'2v2 random' mean that you will randomly be put on a team for each ladder match.
And '2v2 team' is where you are partnered up with someone and you stay their partner throughout the ladder. Most commonly a friend. The only way I believe to set this ladder up, is to have your partner be in your party before starting a 'Quick Match'. You will get placed in different ladders with different friends, meaning you can be placed in several '2v2 team' ladders.