The 380 round is known as a 9mm short. No the 9mm luger, parabellum, whatever is not interchangable with the 380.

380 is a round that has ballistics like a 38 special, a common revolver round. 380 ammo does not have enough energy to lock a slide back so they use a blow back design. It is generally a lower recoil than the nine but a lot of that depends on the gun.

380 ammo is expensive compared to the 9mm brother. it is not a bad round at all but many will advise it too weak and too expensive to consider.

now for my unsolicited advice.

I would suggest that rather than getting a 380 to carry, get a j frame smith. load that thing with low recoil hollow point federals for carry and practice with plain old white box winchester or whatever else of quality is on sale.

I don't know what country the Astra hails from. The .380 is also known as the 9mm kurtz ("short" in German) so 9mm "c" might be an abbreviation of that designation in another language. It was and still is a popular caliber in Europe for pocket pistols.

A j-frame smith is hard to beat but, as long as the gun is reliable, a .380 is perfectly acceptable. I load my own up to pretty hot +P pressures for my PPK and I certainly wouldn't feel underpowered with it.

The Astra gun company from Spain got some of their gun technology from Germany for some of the models they manufacture. I guess that's why it reads .9mm C. In spanish, "short" translates into "Corto" Now everything is making sense. I'll stick to my stainless Ruger .357 Magnum Security Six with a 2.75" barrel to carry and my Remington Marine Mag 870 Shotgun for home security.
Thanks for the info.