Some .38 S&W revolvers sold to the British (actually given to the British in leu of repayment of funds advanced to S&W for development of an S&W SMG the British had contracted for but which was a failure and not acceptable) used .38 Special barrels but a .38 S&W cylinder.
The revolvers had been manufactured as .38 Specials in large runs for expected police contracts that never materialized due to severe budget cuts by most police departments in the late thirties.
To meet the British military's needs they pulled these pistols out of storage and replaced the cylinders with .38 S&W cylinders so the British .380/200 cartridge could be used. By then the British .380 revolver cartridge had been reconfigured for use with a 170 grain jacketed bullet.
It was found that the tighter bore of the .38 Special barrel gave better accuracy with the British cartridge than the slightly larger diameter bore of the Webley and Enfield revolvers.
I expect this was because the newer lighter jacketed bullet did not bump up as well as the heavier lead bullets had done.
Anyway this is why some .380/200 S&W revolvers have barrels marked as .38 Special. Also if rechambered for the .38 Special these would have the proper barrel marking for that cartridge but would produce fired cases with the distinctive bulging of the case near the base.