John Browning designed the .380 ACP (9mm Kurz, 9x17mm) in 1908. It uses the same bullet diameter as the 9mm Luger in a shorter, lower-powered case.
The .380 makes sense when concealment is the top priority. Choose a modern load tested for adequate penetration, because the lower power leaves less margin than 9mm.
Tiny .380 pistols can be snappy and harder to shoot well than a slightly larger 9mm. Shoot both before you decide, and practice with your carry load.
Always use only the ammunition marked on your firearm’s barrel or slide, and follow the manufacturer’s guidance.