I call the cartridge the .38 S&W. What you call it is also correct, but I like to give credit to the Fine American company who first made the round.......
Smith & Wesson.
The .38 S&W is a revolver cartridge developed by Smith & Wesson in 1877. Though similar in name, it is not interchangeable with the later Smith & Wesson .38 Special cartridge due to a different and shorter case shape and slightly larger bullet diameter.
The British military adopted a loading of this cartridge as the Cartridge, S.A., Revolver Ball, 380 in, MkI 38-200 with the "200" referring to the weight of the lead bullet in grains. In 1937, this cartridge was replaced in British Service by the Cartridge, S.A., Revolver Ball, 380 in, MkII. The main difference between it and the previous round was that that it had a 178 grn. FMJ bullet.