I've always been confused by this as well.
As far as I can tell the technology alliance, military alliance and cultural alliance don't do anything.
The exploration treaty is mutual, but in trade the AI acts as if it is not and will trade a large amount of credits if you offer it and demand a large amount of credits if you ask for it.
Based on what I've been told but, haven't actually tested it.
Exploration Treaties are mutual but, as Yeller stated the AI acts as if it's one sided and if you offer will provide you a lot of value for the trade, if you suggest they provide it to you, then the AI demands a large amount of things from you.
Non-aggressive Treaties are mutual but, same as above.
Free Trade Agreement, for what I've been told are one sided and only provide bonus to player receiving not player offering. I haven't tested as typically the AI doesn't have this to offer and I'm just offering. The human player get's no bonus to economy when offering to AI. This has been discussed in multiple threads, however, I haven't seen anything official from Stardock either way to say if this is a bug or acting correctly. It also appears if it does work it does not stack. Mind you I may have missed some comments.
Research Treaty, Same as Free Trade Agreement.
Culture Treaty, Same as Free Trade Agreement.
From what I can tell it's just on "paper" and, doesn't do anything just something put there to look good and pretend it has value except for Exploration treaties in which in larger maps with many players actually is tied to longer turn times because from what I can tell the way the game reveals FOW, also directly causes choppy ship movement. Only thing I have seen is they haven't seen this in house but, they don't have time to play larger games and establish exploration treaties with 60 AI at the same time. I feel for them the game has many possibilities and many players don't play the game the same.