Are you sure you aren't confusing the .380 ACP (a rimless cartridge) with the British name of .380 sometimes used to describe the .38 S&W military cartridge?
Although this just might actually fire, as already mentioned, accuracy would be attrocious. The .380 ACP uses a .355 diameter bullet. The .38 S&W uses a .360 dia bullet. Sometimes you can get by with reloading .38 Special sized cast bullets (.357 or .358) in a .38 S&W barrel, but the small .355 bullets would most definitely allow gas blow-by and probably just tumble toward your target.
I have heard of some people shooting .32 ACP cartridges in .32 S&W chambers, but this is not advisable either.
Chris