The .38 Short Colt was the same size as the old .38 rimfire, which in turn was adapted to conversions of the .36 caliber percussion revolvers. The older cartridge was called a ".38" because it was the somewhat rounded up diameter of the old heel-type bullet, and just sounded better than, say, ".3774 or thereabouts".
The number stayed when the cartridges went to inside lubricated bullets of a smaller diameter, about .357. So why, then, call the .357 Magnum a .357 instead of a .38 Magnum? No special reason; it was just part of the hype built up around the S&W .357 Magnum when it was introduced in the 1930's. Other parts of the hype were the word "Magnum" itself, and the "Registered Magnum" to let each buyer (within limits) have his own custom revolver for the (then) very high price. After all, ".38" was old hat; ".357" was new and up to date.
"Magnum", Latin for "large", was originally applied to one size of champagne or wine bottle. The term was first used in firearms by Holland & Holland for their large necked cases, which reminded someone of those big bottles. S&W's cartridge had no neck, but they focused on the cartridge power and, more important, trademarked the word "Magnum" for a revolver cartridge. For many years, that kept anyone but S&W from using the term on guns or in advertising.
Jim