Unless you have thrown B I G bucks at the swaging die, it will be intended to cold form soft lead -- pure, perhaps 19 parts Pb, 1 part Sn.
Cast balls can be of any lead-based casting alloy you have, the proviso being that the higher percentage of alloy, the larger the cast balls out of the mold. Casting Lyman #2 will yield RBs as much as .005 inch larger than Pb.
I believe most will agree that well-made swaging dies yield more nearly perfect projectiles than comparably well-made casting molds.
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And now for the most important difference -- initial set-up costs. Swaging dies are more expensive than RB casting molds. Swaging dies may require a "bullet" press specific for the job @ hundreds of dollars, or a heavily reïnforced conventional "O" or "H" reloading press.
Some swaging dies intended for black powder target rifles may be set-up differently. The forming impulse may be a solid blow with a heavy mallet rather than pressure via a loading press. However, the high cost remains.
Hope this helps.