Shell holders are different, too. I sometimes end up with a 380 case mixed in with my 9mm Luger cases (despite diligent efforts to separate the two,) and when one starts through my Lee Loadmaster it always screws things up. The shell plate will push the case into the sizing die, and usually will pull it out, but as it moves to the priming stage the case usually starts to slip (or tip) out of the shell plate, but not until after triggering the primer feed. So I end up with a loose case and a primer ready to feed on the upstroke, which I have to stop and retrieve.
Lee dies for 380 are not very expensive, and include the properly sized Factory Crimp Die which makes for some very reliable ammuniton.