44 WCF (Winchester Central Fire) is the original cartridge name. Other makers, such as Marlin did not want the word, or initial of Winchester "W" on ther rifle, so it was renamed 44-40 by other users.
Smith & Wesswon did chamber 44 rimfire Henry in their contract revolvers for Turkey during the Russo-Turkish War. They sold the 44 Russian to Russia and the 44 Rimfire to Turkey... They both paid in gold, so S&W sold to both sides.
Don't confuse 44 centerfire (American), 44 Henry rimfire and 44-40/44WCF, they are three completely different cartridges.