What is the difference between contract theory and mechanism design? Can someone explain the difference between contract theory and mechanism design?
Contracts are a subset of all mechanisms where agreements are enforcable.

An example of a mechanism that is not a contract: 
A second price auction (or Vickrey auction) is a truth-telling mechanism where the enforcability of contracts is not required. In the truth-telling equilibrium no one has any incentive to change their bid, no matter the outcome. This is not because changing the bid would be a violation of contract and result in penalties.