The .380 is a 9mm bullet in a shorter case. 9x17 vs. 9x19. Know in Europe as 9mm K (Kurt or Kurts is German I believe for short), 9mm Corto Italian for short and so on. Might have the spelling wrong but you get the idea. Interesting story about a 9mm Beretta 92 9mm.
I had said 92 out to the range one day along with my Kel Tec .380. I was loading up mags and shooting. The Beretta was going boom, boom, pop??? The slide barely moved and the round that popped ejected the spent case. I had always heard the Beretta's open top design would damn near shoot anything. Well somehow I mixed a .380 in with a mag of 9mm and it feed, fired, and ejected it. impressed the mess out of me. And as far as 9mm goes their is 9x17 (.380), 9x19 (Makarov cartridge), 9x21, 9x23, 356TSW, and on and on. Not to mention the latest incarnation of the mid bore 9mm the .357 SIG. Not sure but I think the .38 super is th 9x21. And then their is the 9mm Largo, 9mm Styer, and I'm sure I'm not getting them all. Sure have played with the fast mid bores over the years though.