AFAIK all S&W centerfire swing-out cylinder revolvers were made with shouldered chambers.
The tolerances for the diameter of .38S&W and .38Spl chambers overlap to some degree. .38S&W cartridges will fit in some .38Spl revolver chambers, but the fit will be very tight, and it may take a hard push to get the cartridge in all the way- IF it will go in all the way.
.38Spl cartridges will fit very loosely in a lengthened .38S&W chamber. When fired, the cases may be hard to extract, due to radial stretching or bulging in to the oversize chamber; IOW the cases may not "spring back" as intended.
.38Spl cartridges will project almost 1/4" from a non-lengthened factory-original .38S&W chamber. This will render the cylinder impossible to close.
I realize that "loose" and "tight" are difficult to define on the Internetz, but it's the best I can do.
...I believe that the British also obtained S&W revolvers that were made for .38 Special. I am not sure about this....
I am not aware of the British having obtained such revolvers, and I've read quite a bit about this subject. The Brits did not have .38Spl ammo in their standard military supply chain, so it would be impractical to use them.
OTOH the American military DID use a good number of the .38S&W revolvers from Lend-Lease production overruns; the Americans likewise did not have .38S&W ammunition in their standard military supply chain, but the guns were largely issued to security guards at non-critical stateside facilities, so the guard could buy his own ammo at the local hardware store.