what the difference?
CRC refers to a specific checksum algorithm. Other types of checksums are XOR, modulus, and all the various cryptographic hashes.
Check out HowStuffWorks for a good description of both and how they differ.
From the page:
Cyclic Redundancy Check (CRC)
CRCs are similar in concept to checksums, but they use polynomial division to determine the value of the CRC
More info is given at the link above including an example of how a checksum is calculated.
CRC (Cyclic Redundancy Check) is a type of checksum, specifically a position dependent checksum algorithm (among others, such as Fletcher's checksum, Adler-32). As their name suggest, these detect positional changes as well, which makes them more robust - thus more widely used - than other checksum methods.