getting most aluminum's density to vary very far from 2.7 gram/cc is a pretty good trick, best done by alloying, not forging. I think the common Generic Description of forging's "density" advantage may have origins in the "grain density" = small grains compared to a basic cast part.
Tighter (less) clearance is made possible by any of many features of piston design. Rarely is a feature strictly connected to the manufacturing process, so saying "forged" does not really "define" everything about how a piston is made. Some Examples are -
- Flexibility - might be from curvy skirt profiles, unsupported tails, or slits in the skirts like olden days.
- Different expansion rates for different materials (old iron pistons were set up pretty tight). The shinier California forged pistons are higher expansion alloys than the dark gray TRW/Speed Pro/Wiseco/Mahle/Kolbenscmidt forged pistons.
- oil return slots rather rather than oil return holes in or near a 4 stroke piston's oil ring groove. Slots make the piston weaker, but keep the skirt cooler and let it operate more independently from the hot swollen piston head. Probably provides flexibility at the skirt top too.
-Including steel expansion fighting struts in the piston. This strut trick is pretty much limited to cast piston technology. See >>one<< version of it here on old Harley pistons.
The forging process kind of precludes including anti-expansion struts. If the application is real Heavy Duty or High performance then the strength enhancing/expansion provoking features of oil groove holes rather slots are likely to be included. The result would be forged piston that would probably need greater cold clearance.