Are the projectile the same for 380 acp and 9mm?

Yes. This is why in Europe the .380 is known as the 9mm Kurtz (German), which translates to "short". The bullets are exact in diameter, but the casing is shorter. It is possible to fire the various weights in each weapon. However, "short" translates to holding less powder, thus being less powerful. Lighter bullets are used in the .380 to attain higher velocities with less powder.