So at least here on this forum:
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.
It's not "just here on this forum". It's in Murray's, the original catalogs, and is going to be anywhere that people have read any modern 99 reference.
Murrays 3-13, Model 1899A Short Rifle, 22" BRL (1905 - listed as saddle gun)
Murrays 3-75, Model 99-A Saddle Gun, A REINTRODUCTION OF THE 1899/1920 22" BRL 1899-A SADDLE GUN
And both the 1899A and 1899A SR have standard weight barrels, the 1899A is 26" and the 1899A SR is 22".