Rem2035 has it right. Good job.
I'll just add that the .32 Remington is a rimless version of the .32 Winchester Special, which was offered in lever-actions made by Marlin and Winchester.
If I recall correctly, the dimensions of the two cartridges -- aside from the rim differences -- are so alike that you can use .32 Winchester Special dies to reload .32 Remington cartridges.
The first cartridge I ever reloaded was for the .32 Winchester Special in a Lee Loader, about 1971.
I still have the rifle, a 1940-made Winchester 94 carbine, but gave up the Lee Loader years ago. Wish I'd kept it, just for sentimental reasons.
Anyway, back in the 1970s I can recall reading that .32 WS dies can be used to reload the .32 Rem, but each requires a different shellholder. Likewise, I recall reading that .25-35 and .30-30 dies can be used to reload .25 Remington and .30 Remington cases.
Never tried it myself so I can't vouch for its efficacy. However, if someone out there has a .25, .30 or .32 Remington and doesn't want to spend $60 to $80 for specialized dies, they may want to compare case dimensions and try it. Could save you some bucks.