There's a 32-20 and a 32 Winchester Special.
The 32-20 is 32 cal 20gr of blackpowder. I see .311, .312, .313 bullets even .315 bullets if the rifle requires it. 100gr jacketed and 115gr lead are common size bullets. 16k CUP pressure and 1000fps is common, although Lyman says some rifles can handle the 18k CUP pressures and 1600-1800fps or so velocity. Load data is interesting to read as IMR 4198, AA 1680 fast rifle powders are common as are #7 and #9 pistol powders, even HP38(fast pistol). My neighbor has a Ruger pistol in the caliber.
32 Win Special has 170 gr common size bullet.