Jim Watson is correct on the .45 Schofield, sometimes called the .45 Government or .45 Colt Government. When the S&W was adopted, the government had to adopt new ammo because the standard .45 Colt was too long for the S&W chamber. The rim of the new ".45 Government" was the same as the Colt rim but the case was short enough to fit the S&W. So six rounds could be loaded in the Colt, and only one type of .45 ammo had to be issued for both guns.
When the Model 1909 swing cylinder revolver was adopted, though, its ejection system needed a larger rim than that of the old .45 Colt or the .45 Government. That led to the adoption of the Model 1909 cartridge, which is nearly identical to the .45 Colt except for the larger rim; it can be loaded in the Model 1873 but only in every other chamber. This was of no concern to the army, since by 1909 the old single actions had been withdrawn from service, but it bothered civilian shooters.
Just FWIW, the rim size didn't matter in the SAA Colt, since the rim was only needed for case support in firing. Ejection was by ejector rod. Colt did run into a problem when English dealers wanted SA Colts in .476 Eley* and .455 Eley*, which had normal rim diameters. So Colt took the unusual step of making the cylinder window and the cylinder oversize, then drilling the chambers at an angle, so that the rims would fit without altering the position of the barrel and center pin. It evidently worked; Colt sold a fair number of guns in the two calibers.
*The cartridge is normally called the .476 Enfield. It uses the same case as the .455 Webley (.455 Eley), but a larger diameter heel type bullet. For some reason, Colt called both cartridges "Eley" after the British ammunition maker rather than the gun maker. They even carried this custom into the auto pistol era, when magazines for the .455 Webley Auto caliber contract pistols were marked ".455 Eley".
Jim