The .44 Remington C.F.
I have only one specimen of this round in my collection, and I suspect it is a reload, as the bullet appears to be cast, not swaged. The unmarked case is clearly by E. Remington, and dimensions clearly put it as the .44 Remington.
Only one gun was chambered for this round, the Remington 1875 Army revolver. Don't be misled by the name, the gun was never used by the U.S. Army. I think it was submitted, but the Army already had Colt and Smith & Wesson revolvers in service by then, and certainly they weren't interested in introducing another cartridge into the supply chain.
White & Munhall, in their work, state that the .44 Colt cartridge could be used interchangeably in this revolver. But in their work "Remington Handguns" Charles and Carol Karr state that though the two rounds were similar, they were not readily interchangeable. Some .44 Colt rounds would fit some Remington revolvers, but full interchangeability was not possible.
.44 Colt rounds produced by Frankford Arsenal have box labels reading "For Colt and Remington Revolvers." This has misled some, as they predate the .44 Remington ammunition by some four years. This ammunition was intended for use in the 1858 Remington revolvers converted to metallic cartridges and still in the hands of the troops, as were the Colt cartridge conversions. Until these guns were phased out, Frankford Arsenal was making the .44 S&W (American), the .44 Colt, and the .50 Remington. All were officially replacedby the .45 Colt in 1873.
The .44 Remington cartridge was short lived, and I believe only E. Remington made the round. The last Model 1875 revolvers were chambered in .44 Winchester and .45 Colt.