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What is the difference between the content comparison / hashing types?

 
From a user perspective, there is very little difference between the hashing algorithms - some people like the choice though.
 
 
Byte-by-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 or byte should be fine for most cases.