When you click CALCULATE, HS asks for a revision date.  This date is very important..."Only Scores with dates prior to or on the revision date are used in the calculation of handicaps."  If the revision date was set differently between the 1st and 2nd time handicaps were recalculated, thus using a different set of scores for each (some) golfers,  you'll have a different handicap.


For example....
If I posted 10 scores to a golfer dated 9/22 and another 10 scores dated 9/23, and then clicked calculate and set the revision date to 9/22, only the scores dated 9/22 or before would be used in the calculation. Then if I clicked calculate again and set the revision date to 9/23, I would see a different handicap for the golfer because now HS would also use the 9/23 scores.