Needing more loot is pretty much standard for Expert level, but there's also "Don't kill anyone", which puts a whole new twist on playing the game. Sometime extra objectives creep in as well, like recovering a special item.
There's also a fourth difficulty level, but since that's user-defined, it's kinda hard to keep track of it in-game; ghosting. Ghosting involves, but is not limited to:
# Playing on Expert.
# Not destroying anything.
# Not being detected or spotted by anyone (or anything, if you're feeling extra ghosty).
# Not incapacitating anyone, whether it be by sword, blackjack, gas arrows or whatever.
# Leaving everything as it was. That means not picking up anything needlessly, closing doors and windows behind you, locking doors you previously unlocked (if possible), etc.
In short, to get the job done without anyone ever having noticed you were there, and leaving no trace of you having been there.
Of course, some missions simply cannot be ghosted, which leaves some puritans constantly pissed, and there's one mission in Thef 2 that makes ghosting mandatory.