> A .38 is the same diameter as a .357.
Not just diameter, the bullet itself is identical. The cartridge is longer with more powder in a .357, which makes it a good bit more powerful in practice (2 to 3 times as much energy).
The explanation for the caliber discrepancy is halfway interesting:
"Despite its name, the caliber of the .38 Special cartridge is actually .357 inches (36 caliber/9.07 mm), with the ".38" referring to the approximate diameter of the loaded brass case. This came about because the original 38-caliber cartridge, the .38 Short Colt, was designed for use in converted .36-caliber cap-and-ball Navy revolvers, which had untapered cylindrical firing chambers of approximately 0.374-inch (9.5 mm) diameter that required heeled bullets, the exposed portion of which was the same diameter as the cartridge case."