OK, when you say .38, I'm assuming you mean .38 Smith & Wesson and not .38 Long Colt or something like that?
"When loaded with black powder, do the cartridges retain their smokeless designation"
Well, of the cartridges that you name, only the .357 Magnum was originally developed with smokeless powder.
The .38 S&W, the .38 Long Colt (not sure which one you mean), and the .38 Special were all developed originally as black powder cartridges.
The .38 Special originally held 21.5 grains of black powder behind a 158-gr. bullet.
The .38 Long Colt originally held 18 grains of black powder and a 150-gr. bullet.
The .38 S&W held around 14 grains of black powder behind a 146-gr. bullet.
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