The 38 S&W cartridge is essentially what the British called .38/200 or sometimes called .38 Short. The bullet is a true .38 caliber, unlike the .38 special which is .357 in diameter. My father had a .38/200 Smith & Wesson "Lend-Lease" service revolver that was shipped to Great Britain by the United States as part of a massive foreign aid package that included everything from ships, aircraft and tanks to small arms and field equipment.
My father was in an American unit that was formed overseas very early in the war so their weapons were a mixture of '03 service rifles retrieved from U.S embassies in occupied Europe and British supplied sidearms. The Brits asked that the medium frame Smith & Wesson -- what would later be designated as the Smith & Wesson Model 10 -- to be built with a 5" narrow barrel, deep blue finish, and diamond checkered walnut grips and blued lanyard ring.
When America entered World War II, the War Department continued to furnish Great Britain with that same revolver in .38/200 while making a similar version with 4" narrow barrel, Parkerized finish and a .38 special chambering as an augment sidearm for American forces. The American version was referred to as the "Victory Model" and some 900,000 of them were made. Many servicemen that had .38/200 "Lend-Lease" service revolvers brought them home after the war since they were not officially in the U.S. inventory. My father had his and carried it with him during my growing up years until the late 60s when it was stolen from the house by a drifter.