You have a .32-20 Hand Ejector Model of 1905 -3rd Change made in between 1909-1915. Perhaps if you could be more direct about what questions you have we can attempt to answer them. While it appeared in the black powder era in Colt's revolvers and Winchester lever actions it transitioned to smokeless. Colt and S&W chambered revolvers in the caliber past the first world war, it largely played out by WWII. Since it also transitioned to rifles there are "rifle only" cartridges out there, don't shoot them. The cartridge has enjoyed a limited revival in the past generation.
The .38 Special pretty well eclipsed the .41 Colt, .38 Long Colt (its parent) and the .32-20 (.32 WCF, .32 Winchester).
Very nice looking 32-20. The pic below shows an older box of ammo is on the left. The newer ammo marked on the right as 100 grain lead round nose is ok for the older guns per Winchester techs. I have used it in mine with no problems and it is from 1917. It is a great cartridge. Enjoy it.