Depends where you look!
On the scorecard, only putts with putter(!), starting from the green(!), will count, while in the game stats, anything with putter AND anything on the green do count.
Edit: Oops, I mixed it up:
On the scorecard, anything with putter AND anything
on the green do count,
while in the game stats, only putts with putter(!), starting from the green(!),
will count,
Putts from the fringe are the most usual source of discrepancy AFAIK.