You sure can use 9mm and 380 bullets interchangeably, but there are trade-offs.
As pointed out, heavier 9mm bullets will need to be seated carefully. Certain ones, like FMJ-RN, might need to be seated so low the ogive goes into the case mouth preventing a proper crimp. FMJ-TCs will work better in this regard. Regardless, it will seat deeper, so take the advice above, and be prepared to load your powder charges down.
I've loaded 122gr lead RN bullets in 380, but there are a lot of variables to keep track of - basically everything mentioned above, but with even tighter tolerences.
JHP bullets generally are shorter in their out-of-case dimension, so a 9mm 115gr JHP-TC will usually fit, but don't expect it to expand. It will drill a .356" hole through the target...
Another way to go is to load 100gr 380 bullets in 9mm. Again, won't be perfect, as the screaming-fast loads will over-expand (blow up) if you use expanding bullets, and if you use FMJs, they're typically blunt-nosed (better for the 380), so they'll work better in 9mms which are forgiving of the shorter OAL loads.
So, bottom line is that both ways work, but neither is ideal, with their own difficulties.