Doing some online research here is some Info. I found:
Be sure to read the bottom part
The .38 Smith & Wesson is even older than the .38 Special, with the former having been invented in 1877. While it never reached the sheer popularity of the Special, the Smith and Wesson take on a .38 round found important military contracts, especially among the British and their then imperial holdings. While it has fallen out of favor since, the .38 Smith and Wesson was in wide military use in both world wars, as well as the Korean war.
In terms of specifications, the .38 Smith and Wesson shoots a bullet of around 175 grains at somewhere around 700 ft/second, depending on the particular loading. Compared to the Special, the Smith and Wesson is a heavier, slower-moving round that functions on lower pressure. It’s for that reason that they’re not interchangeable.
38 S&W vs 38 Special
The .38 Special and the .38 Smith and Wesson are not interchangeable. The .38 Smith and Wesson is larger in diameter than the .38 Special. That makes it physically impossible to chamber a .38 Smith and Wesson in a .38 Special gun in most cases. An exception to this is in cases of ammo that is out of spec, or if a cylinder is particularly worn in a revolver.
Because it is smaller, you can fit a .38 Special round into a .38 Smith and Wesson Gun. This is, however, a bad idea. If the gun is an auto-loader, it likely won’t function at all. You may be able to fit the smaller round in a revolver, but, in the unlikely case that you can manage to keep the round in place and the round goes off when struck with a firing pin, it will almost certainly rupture the case.
That would cause a lot of hot gas and shrapnel to form, and it has to go somewhere, likely into the shooter. Thus, even if it physically fits, it is in no way a good idea to attempt to interchange these cartridges. With that said, both of them are interesting and certainly have a place in the handgun world.