I suppose, that they both are Remington samples. The shorter is cca. 40-45 Rem. 2,1" and the longer is 40-60 Rem. straight 2 1/4".
I checked James Grant’s book Single Shot Rifles and found that the Remington version of the Sharps .40-70 straight was in fact called the .40-65 Remington. Remington also offered the Sharps .40-50 straight as the .40-45 Remington. This case is very similar to the .40-65 but is only 1.875 in. in length, compared to 2.5 in. for the .40-65. Both these cartridges were primarily used in the Remington Hepburn rifle. Jack
The pictured cartridge with the 2.3125 in. case length appears to me to be a .40-65 case shortened about .2 in. and loaded with a pistol bullet. Jack