As I recall the 45/70 was originally black powder and in modern firearms is loaded with smokeless powder. It replaced the 50/70 which was the Army cartridge after the civil war till 1873. Both were centerfire. The rifle, the Model 1873 single shot Trapdoor Springfield used the 45/70 loaded with 70 grains of black powder. the Carbine load was loaded with 55 grains of black powder, if I recall correctly.
Upon further research I found the 1876 Carbine issued to the Mounties was 45/75, not the 45/60 as I originally thought. Still the 45/60 was a popular round in the day.
I'm not sure what you are finding with the rimfire, perhaps Spencer or Henry rifle cartridges, both saw lots of use out west.