From the OP, I thought this was just about the seating die. For sizing, you will not quite get a match. The .380 is not only straight, but it's maximum OD is about 7 thousandths smaller than that of the 9 mm Parabellum using SAAMI standards. This means that unless a .380 case has full maximum wall thickness, a carbide 9 mm sizing die cannot be certain to make it small enough to grip the bullets. A steel 9mm die almost certainly won't do it as a steel 9 mm die preserves the 9 mm case taper, where the carbide dies just size them straight. You see complaints about the bullet base bulge as a result.
A .380 carbide die will size a 9 mm case more than necessary, wearing the brass out sooner, but it will probably work for a few cycles, especially if you lube the brass. I once ran a piece of .45 ACP brass into a .44 Special/Magnum sizing die by mistake. It slid right in, but didn't come out looking very promising. I should probably find that case and flare the mouth back out and stick a .45 bullet into it to serve as a reminder.
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