So what would happen if I accidentally loaded and fired a 380 (with a 9mm powder load) in my 9mm semi-automatic?
Nothing good!
IF it even fits, 9mm powder loads are about 25% more than .380, and combined with the difference in case volume,
significantly higher than normal pressure should be expected. I don't know how much, but it could easily be into the range that would damage your gun, and possibly you!
Proper inspection of your brass before, during, and after the loading process will prevent that.
If you are running a progressive press (and particularly with a case feeder) inspection of each piece of brass before loading the hopper is important.
Additionally, progressives don't have the same "feel" feedback as single stage presses. The .380 and the 9mm use different shellholders, so a .380 case probably won't be held properly.
The .380s specs smaller than the 9mm, so its going to feel unusaully "easy" going into the sizer die. The shorter case isn't going to work a powder through expander die the same way, likely resulting in less case mouth flare, and possibly an incomplete powder dump.
The .380 run though 9mm die settings might not be flared enough to easily seat a bullet, and of course, if it does, its not going to be seated to the correct depth in the shorter case.
All these things should be either tactilely, or visually evident, but a progressive press can make them difficult to feel or see, unless you are specifically looking. If you do manage to miss them and load a .380 case with your 9mm setup, the resulting round should be very obvious compared to the other rounds loaded.
You are the only QA/QC that your reloads get. Sorting and checking range brass is an important step to prevent problems later in the loading cycle.
Generally speaking, when a .380 fires in a 9mm gun, its being held in place by the extractor. This usually doesn't damage the gun but may or may not cycle the action, depending on the gun.
Overcharging a .380 case with a 9mm powder charge would be a BAD THING.
Keep a close eye on what you're doing, and be safe!