"Casting" always involves turning the metal from which the ironhead is to be made into its molten, liquid state, after which it is poured into a mold to form the ironhead design.
"Forging" involves literally pounding or compressing the metal, in its solid form, from which the ironhead is made into the designed shape of the ironhead, after which a number of other machining and drilling steps are necessary to complete the production of the ironhead.
If you have a cast iron and a forged iron of exactly the same shape and weight distribution design, the same loft, the same center of gravity position in the two heads, and the heads are built with the same shaft, same length, same grip and same swingweight/MOI, hitting the same ball, the shots will fly identical distances and 99-percent of all golfers will never know which was forged and which was cast.
Most of the remaining 1-percent want to believe that the forged iron would be softer in feel because the carbon steel of a typical forging is a softer metal, but scientific research has shown that the hardness difference in a metal alone is not enough to create a difference in impact feel. All of the other factors listed above are the reason for differences in the feel of shots hit with one club vs. another.
In other words, it's not the fact that this iron is cast and that iron is forged that makes them feel different hitting golf balls, but rather the other design elements (forged irons are typically more expensive than cast, and so are aimed at better golfers - that means less or perhaps no cavityback, less perimeter weighting, and so on).
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