Data each bureau collects may be slightly different. For instance, you might have an old car loan from a company that reported only to one of the bureaus. The other two are missing that "tradeline."
The score algorithm (formula) is different between the three bureaus because the data they track of is not the same. For instance, Equifax counts the number of bank or national revolving accounts with balances, while TransUnion does not.
Experian goes to great pains to promote anyscore BUT the FICO. But when they have to write pretty for Yahoo!, they jump right on the FICO bandwagon: 33 factors.
Fair Isaac suggests using the Reasons delivered with a score in notifications of denial of credit.
Somewhere along the line, the scoring system began providing up to five "score reasons," rather than four.