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In swaging bullets, you will always be putting a smaller diameter object (lead, jacket, or a combination of both) into a slightly larger die cavity or hole. Each step in swaging increases the diameter of the components, until they reach the final diameter in the last die. Swaging never reduces the diameter. You will only have stuck bullets and hard ejection if you try to push a slightly larger part into a slightly smaller hole. This is the difference between swaging and drawing. You never swage anything "down". You never draw anything "up".

In drawing, you do push a larger part through a smaller hole, to reduce the diameter. This kind of die is a ring, not a cylinder closed on one end. The jacket or bullet that you are reducing is pushed through the ring, and is decreased in diameter when it comes through the other side.

We use drawing to make longer, smaller caliber jackets from shorter, larger diameter ones. Also, within some narrow limits, it is possible to make a smaller caliber bullet from a larger one, although this degrades the quality of the bullet unless very special conditions are observed. Usually the difference in diameters has to be within 0.005 thousandths of an inch when you reduce finished bullets by drawing. Jackets can be drawn much more than this