So at least here on this forum:
The later 99A made from 1971-1982 is generally referred to here as the "Saddle Gun".
The 1899-F Carbine made from 1899-1919 we refer to as the "Saddle Ring Carbine" or SRC.
The 1899-A made from 1899-1922 and listed as the "Saddle Gun" we call the "Short Rifle" or SR.
There is also a 1899-A Standard Weight Rifle made from 1899-1926ish.
Simple.