Well, you're both right, partially.
There are various algorithmic models unique to each bureau and subscribers can, and do, request certain ones for their own analysis.
In broad terms, a tri-merged report for the purpose of mortgage credit is going to use different models than one for financing a new car for example.
Typically, however, the score seen here on myfico is Not the same algorithm used for a mortgage so is different.
All that being said, at least you get an up to date version here of generally what is going on with your score. The more knowledge about what makes scores move, the better!