Maybe I'm out of touch about this.
My Speer reloading manual shows the .38 S&W using the same projectiles as the .38 Special -- lead bullets sized .358" and jacketed bullets sized to .357".
Test firing was done in an S&W Model 33 with a 4" barrel.
Speer cautions that due to the low powder volume, jacketed bullets heavier than 125gr are not recommended. If you use the 148gr bevel-base wadcutter, it needs to be seated with the top grease groove exposed instead of flush (or nearly flush) with the case mouth.