When Winchester developed the cartridge for their 1873 lever action rifle, they named it "32 WCF". I believe that Marlin chambered their rifles for the same cartridge and called it "32-20", so they did not have to stamp a reference to Winchester on their rifles.

S&W stamped 32 Winchester CTG on the early revolvers and 32 W.C.F. CTG on the later ones.

Since it is originally a rifle cartridge, ammo manufacturers and reloading component manufacturers usually list the cartridge in the rifle category. It is safe to shoot modern factory ammo in these old guns. But it is always a good idea to have a gunsmith inspect the gun first.

Earlier this summer I shot one made in 1915 in a club handgun steel plate match. Lots of fun to shoot.

The Model of 1905 4th change was manufactured from 1915 to 1940.