A file hash is an (virtually) unique string of numbers and letters which is calculated from the contents of a file.  It can be thought of as a fingerprint.  The advantage of this is that it makes comparing files much quicker because you only need to compare the hash fingerprints.

 

Duplicate Cleaner implements several different file hashing algorithms.  From a user perspective, there is very little difference between most of the hashing algorithms.

 

Direct Comparison-

Cryptographic hashes-

 

Non-Cryptographic hashes-

 

Byte-to-byte would be considered the most exact as it compares each file "byte-by-byte". The other methods use hash fingerprinting. MD5 is the fastest, but has the highest chance of a "collision" (i.e. two different files of the same size getting the same fingerprint). This chance is still remote though (billions and billions of files), so it's not a major concern.

In summary, very little practical difference (but the SHA ones are slower). MD5 should be fine for most cases.