commonlaw:I think they certainly discern stroke types for purposes of stat tracking.
The official rules don't know stats at all.
Also, they don't know "putting", only "strokes on the green" etc.
Putts from the fringe that are holed count in your stats but not your putting stats. They are counted as a holed approach shot. That is why when you hole out a putt from the fringe you will see in your activities that you holed a shot from x number yards