They are not swages, because bullet swaging always expands or increases the main bullet diameter in every step.
Drawing is simply pushing an object through a hole, so it comes out smaller.
Corbin builds two different kinds of draw dies. In this style of die, there are two versions. The jacket wall can be made thinner, or not, depending on the clearance between the punch and the die walls. A pinch trim die for jackets has a punch with a shoulder joining two diameters. The first diameter fits into the jacket after it has been reduced.