The .38/200 is a completely different case from the .38 Special. The .38/200 was the British service round for many, many years, but it was never really a major U.S. round, and while we can't say that it never walked around in a GI's holster, it was never a service cartridge of the U.S. military. S&W marketed a cartridge called the .38 S&W which is remarkably almost identical to the .38/200 (imagine that!), but the .38 S&W Special is actually based on the .38 Army round.
Many, many S&W K-frames were chambered for the .38/200 (or .38 S&W), especially Victory models that were lend-leased to the UK during WWII, and there were commercially marketed ones to boot. Colt used to chamber guns for it as well. You can still find .38 S&W rounds around. In fact, the swap meet I wandered through last weekend had a guy selling all kinds of vintage rounds, including about 10 boxes of .38 S&W. (If I actually owned something chambered for it, I'd have been happy as a pig in mud.
) .38/200 is still in service in some of the UK's former colonies as a police and military round, and used to be just as dominant in many of those colonies as .38 Special always has been here and many other places, especially South America.
.38 S&W Special is higher pressure, slightly smaller diameter, and longer OAL than the .38 S&W. They are not compatible cartridges. The .38 S&W is not a .38 short that can be fired in the .38 Special chamber, as .32 Longs can be from .32 H&R Magnums, or even .38 Specials from .357 Magnums.
The .38 S&W Special (commonly shortened to .38 Special, especially on Colt's revolvers and boxes of ammunition, but always marked ".38 S&W Special" on S&W revolvers) has its true roots in the cap'n ball era. The .36 Navy Colt, a cap'n ball revolver, was actually .36 caliber or thereabouts. When companies started to do cartridge conversions of those guns, various cartridge designs were attempted. Some were heeled bullets, some inside lubricated, but they all kept on with the nominal .36 caliber.
When the Army decided in the late 1800's to switch to a lighter-kicking revolver than the .45 Colt SAA, Colt submitted a double-action, swing-out cylinder revolver very similar to what we use today. It was chambered for what they called the .38 Long Colt, which had its roots in the old conversion guns Colt made before S&W's patents on modern cylinders expired. The chambers were not stepped, but were through bored. I have never seen any ammunition for these old guns, so I cannot say whether they were heeled or inside lubricated. I recall reading a warning in a very old American Rifleman not to attempt to fire .38 Specials or .357 Magnums in those old guns, even though it is entirely possible to put the cartridges in them due to the through-bored chambers. I can only imagine that a .357 would be like an overpressured proof load. Hand-grenade time, I think.
Regardless, after the Phillipine insurrection, the Army was entirely dissatisfied with the combat effect of the light-kicking revolver's cartridge, and several avenues were tried to step things up a bit. One became the 1911 pistol in .45 ACP, though the design was originally for a .38 auto cartridge that was quite a bit hotter than the .38 Army. Another was from S&W, who added weight to the slug, increased the powder charge, lengthened the case, stepped the chambers, and dubbed it the .38 S&W Special. That load was a .357 caliber, 158 grain, inside lubricated RNL bullet at over 900 FPS from a full-sized revolver, which was quite a jump up in power from the 150 grain/700 fps Army load.
Though the official military loading for the .38 Special was eventually a very anemic 130 grain FMJ, and S&W's "Military and Police" revolver (the original K-frame) was never adopted as the standard issue for any of the major services, it was taken as substitute standard and served in every branch of service, all over the world, through Desert Storm. It was not completely removed from military service until well into the 1990's. Additionally, it was, by far, the dominant police pistol cartridge of the 20th century, and has been used in police pistol marksmanship competitions and bullseye competitions ever since it was introduced.
So, there's some history. The bullets for the .38 Special are .357". They aren't .38" because the Navy Colt was .36". "And that's the troof." (channelling funny-looking clown from 70's children's show).
