The reason I ask is historical in nature.
A light commercial aircraft from 1936 has a semi-elliptical planform and a stated (advertised) area of 185 ft^2.
A later 1939 adaption of the same design has same chord & span, same tip shape, but a slightly wider aft fuselage; this trims about one ft^2 on each side off the wing area at the root. BUT - this later model is advertised as 210 ft^2!
So the only reasonable answer I can conjure is that the rules of the game changed. Drafting the two as accurately as I can, I see the fuselage width times the chord is about 25 square feet. This accounts for the difference in advertised area, even though the effective area is virtually identical. One method includes the 25 ft^2, the other omits this area.
The OP's question puts names to these areas, I guess. 185 ft^2 is the exposed area; 210 is the reference area.