Couple of things you need to remember when comparing cartridges. The .44 Henry was a rimfire. The .44 American, .44 Russian and .44 Colt were centerfire and would originally have been balloon cases. The .44 Special (AKA .44 S&W Special) and the .44 Magnum (AKA .44 Remington Magnum) were introduced late enough that they would have started out as solid head cases.
Rimfire cases will hold more powder than the same size balloon head case which will hold more powder than the same size solid head case. That is because in a rimfire case there is no space inside the cartridge taken up by primer and primer pocket. In balloon head cases there is space around the primer pocket which will hold powder. Solid head cases are solid up to the flash hole.
The old .44 S&W (AKA .44 S&W American or .44 American) would not have been called American until the introduction of the Russian version of the .44 S&W was introduced. Until then it would most likely have been .44 for the S&W Army Revolver, or just .44 S&W. Originally the S&W No 3 was chambered for the .44 Henry until the Army suggested a center fire cartridge would be more reliable. The .44 S&W was developed in response to that. Its slightly longer case was necessary to keep the powder capacity inline with the .44 Henry.
The .44 Russian was adapted from the .44 American, but used a inside lubed cartridge, that is the lube groove were protected by the case and the bullet was the same diameter as the inside diameter of the case. The previously cartridges were outside lubed, heeled cartridges - the base of the cartridge had a shoulder that slide into the case, while the top portion was the same diameter as the case. The .44 Russian case was basically the same as the .44 American, just slightly longer to accommodate the bullet's lube grooves now being inside the case.
A solid head case will hold about 10 - 15% less black powder than the same balloon head case.
Cartridge Bullet BP Cap Introduced
.44 Henry 210gr 26gr 1860
.44 American 225gr 25gr 1869
.44 Russian 246gr 24gr 1871
.44 Colt 215gr 28gr 1871
.44 Special - - 1907
.44 Magnum - - 1950