(Edited 4 years, 2 months ago)

Contracts are one level and you are done at your current character level.
Expeditions are 3 consecutive levels (with each level being 1 level higher than the last), where at the end of each level you can leave, as you only have 3 deaths to complete all the levels in, or you get no production.
Adept Expeditions are always your level up to a maximum of level 40, and have no bonuses to magic find, production, etc.
Veteran Expeditions start at level 40 and can be started at levels increasing in 3's from there (40, 43, 46, etc). Each level you go above 40 increases magic find, production, etc. You unlock the next level group by completing the full 3 levels of the previous set (e.g. complete 40 to 42 to unlock starting at 43.)
I haven't quite finished the first tab of Veteran (which goes to 67), so I can't say what happens after that.

Kerrin Original Comment