Both the .38 Special and .380 ACP use the same bullet diameter (.357).  The differences lie in the kind of case, the case capacity for powder, and the bullet weight that's safe to shoot in the cartridge.

 

The .38 Special is a rimmed revolver cartridge (9x28R to use it's metric designator).  It is usually loaded with a 158-grain bullet (maximum).  The .380 ACP (9x17) is a rimless semi-auto cartridge that's loaded with bullets of less than 100 grains -- usually about 87 grains.  As you can see from the metric desingation, the case lengths are different and that affects the amount of powder the round can accept.  The .38 Special can be loaded much hotter than the .380 ACP for defense purposes.  However, both can put bad guys down if loaded with the appropriate jacketed hollow point bullets.