The original .38s (such as the .38 Short Colt, the great-grand daddy of the .357) were true .38s. As mentioned earlier, they used heeled bullets -- the base of the bullet was reduced in diameter to fit inside the case.
These bullets were lubricated (as all lead bullets must be), and the lubricant grease wore off, washed off, or baked off in the outdoors. The solution was to reduce bullet diameter, add grease grooves, and load the bullet so the grease grooves were below the case mouth. This made the bullet too small for the bore.
There were two choices -- make the chambers and cases bigger, and use a bullet properly sized for the bore, or simply reduce bore size. The latter choice made most sense. The new, reduced size bullets were made of soft lead with hollow bases and would still shoot fairly well in earlier .38s -- to retain that market, the designation went unchanged.
As a result of all this, the .38s became .36s in actuality -- something that Douglas Wesson recognized when he named the new cartridge the ".357 Magnum."