If you are talking about 38 super / 38 super +p ammo (i.e. the head stamp says 38 super or 38 super +p ) then no it is not for use in a 380 in no way shape or form. I will not chamber in the gun... and good thing!! 380 is a 200 and a few foot pounds of energy round, 38 super +p runs 500+ foot pounds. 38 supper and 380 are not the same cartridge!
The only other name for the 380 is 9mm short or 9mm kurtz (german word), one might see this on older imported ammo.
If you are talking about a 380 acp +p as made by companies like buffalo bore then you would have to look in the smith manual and see if they have a position on it, I would be shocked if they were ok with it.
In general the current crop of 380's are optimized for size and easy carry so it's unlikely many makers will endorse their gun for plus P rounds as their size leaves little margin of safety. And frankly who would want to shoot plus P 380 in a small gun? I have shot the LCP, kel tec and carry a seecamp 380, they are enough to handle in 380 with hydrashocks, I'd not want to try it with +p.
Maybe something like the browning BDA in 380 (Beretta 84), Sig 232 or a locked breach gun like the colt pony / sig P238 would do ok with the +p 380 though the buffalo bore sight does list trial velocities for their +p stuff with the keltec. Must be interesting testing that stuff in that light of a gun.