Definition: The contract proof is usually a color proof that is looked on as a contract between the printer and client as the final proof before going to press. Currently the de facto standard for a contract proof is a Matchprint or laminate proof although some high-end digital proofs are considered good enough to accurately predict color from the press.
A contact proof is not the same as a contract proof (unless it's a typo).
Examples:
The contract proof is the one that says to the printer "Everything looks good, let's go to press."
