Hello. This is from memory, but could be wrong: The old original .38's and I'm not even sure of the designation were heeled, ie: similar to a .22 rimfire such that the outside of the bullet was even with the outside of the case and the slightly smaller portion of the bullet after the "step" was inside.. I believe that is about 0.38" or so. As we all know, the .38 Special and .357 magnum bullets do not ride flush with the outside of the case so the diameter is slightly smaller.
Could it be that when the "38" first came into use in the late 1800's the case diameter was what they went by and thus called it a 38. The first one was a Colt 38 long that had a case of .381" diameter and bullet about .361". When S&W introduced their "38special" ammo and revolver around 1902 or so they reduced the case a little and also the bullet. The official case on most reload sites is .379"diameter maximum.
So see what you think about it. Is the 38special .38" specified maximum diameter for the case?
Oh, p.s., I don't know anybody that was around way back then that could tell us for sure. Except maybe Jeff Cooper