[ptomato]

the full name of .38 is .38 Special, and the full name of .380 is .380 ACP. IIRC, .380 ACP was so named to distinguish it from an earlier related design, .38 ACP. In common use, if somebody says .38 they're referring to .38 Special as that's by far the most common cartridge with .38 in it, and if they say .380 they're definitely referring to .380 ACP, though it's also sometimes referred to as 9mm Browning.

ETA: and in the case of both these rounds, .38" is actually the approximate diameter of the _case_ not the bullet; the diameter of .380 ACP bullet is 9mm, and the diameter of .38 Special is .357".