No. Semi-auto, rimless cartridges depend on having the case mouth (where the bullet is crimped into the brass) settle on a rim at the end of the firing chamber. This places the case head (where the primer is placed) in exactly the correct spacing for the firing pin to strike. A .380 ACP (9mm kurz) will slide down into the chamber and stop at the rim. The firing pin can't possible reach the primer. The 9mm, if placed in a .380 ACP chamber will protrude a great distance. The slide will not close and (hopefully) a safety mechanism will block the hammer from striking the firing pin.
This same technique of setting the headspace using the case mouth is also employed in the .45 ACP.
You should never put any ammo into a firearm unless is is specifically designed to handle that ammo. It is dangerous to do so. At the minimum, you may be disappointed when it doesn't fire. The worst case is obvious.
Bullet weights for the .380 ACP range from 85 gr to 110 gr. The .380 ACP uses a .354 caliber bullet. Same as the 9mm. The .38SPL uses a .357 caliber bullet in weight ranges from 125 gr to 180 gr.
That turns out to not be the case, in my experience.