I could be wrong, but I think they're lighter

I've played forged irons for years.  There is no discernable difference in weight of same shape steel clubheads.  Forging gets it shape by pounding near-molten metal into shape...giving the grains (microscopic) in the metal a flow for directional strength and stability.  This allows same strength in a softer metal.  Thus the softer feel of forged clubs.  Cast clubs are made by pouring molten metal into a mold of the desired shape. When it cools the metal grains are small and round (not elongated as in forging). To get necessary strength the metal is made harder (also brittle).  Forged clubs can be readily bent to adjust loft and lie.  Cast clubs may break (more brittle, remember) if bent to adjust loft and lie.

The forging process doesn't allow for cavities to be made easily.  Thus most game improvement and maximum game improvement irons are cast.  Forged irons tend to be for lower handicap players (probably 10 handicap and less).

If you are a feel player...you would probably prefer forged irons.

Swingweight is the measure of the entire club,  head-shaft-grip. Swingweight affects swing speed and feel. You can get the same swingweight in both forged and cast irons.  The clubhead material alone is not an indication of swing speed.