The .38/200 (also called the .380/200) is the same cartridge (dimensionally) as the .38 S&W.
Notice that I didn't write .38 S&W Special, since that is a different cartridge.
I looked at the dimensions just now. The .38 Special is slightly smaller in radius, but longer. The .38 Special fires a bullet of .357 diameter. The .38 S&W fires one of .361 diameter.
So, if the cylinder has a "shoulder" in each chamber the .38 Special round should drop into a gun made for .38/200, but not go in all the way. The shoulder will stop it.
If there is no shoulder in each chamber, then the .38 Special will fit into either gun and this shows you nothing.
If you have an actual .38/200 (or a .38 S&W) cartridge then you can see if it fits. It will not fit into a gun made for .38 Special, I think. But since the difference of the case size is only .0075 of an inch, at the base, it may be that the actual machined size will allow the .38 S&W to fit in the .38 Special gun. There are people on this forum who have actually tried this, I am sure, so maybe one will tell us if I am right.
You ask a good question, since I believe that the British also obtained S&W revolvers that were made for .38 Special. I am not sure about this....
“There’s a rattle in my glove box,
A Federal twelve-gauge slug.” – Adam Carroll in song Porter Wagoner