What is the name for a flap that increases the wing's area but not its camber? Flaps are high-lift devices mounted to the rear portion of an aircraft's wing.


Some types of flaps increase lift by increasing the wing's camber, or, at least, that of its lower surface (plain flaps, split flaps, Junkers flaps).
Most flaps increase lift by increasing both the wing's area and its camber (Fowler flaps, gouge flaps, Fairey-Youngman flaps, zap flaps).


What would one call a flap that increased the wing's area, but not its camber (like the first stage of a Fowler flap)?
Useless flap.

It is always the increase in camber that increases the lift. The reason to increase the chord is that if the curvature was increased too much, the flow would separate and the wing would stall, so the flaps move aft to be able to move down more while still maintain moderate curvature.

The Fowler flaps do move a bit down even in the first step, and the slats move forward and down with (or even before) them, so the camber increases even in the first step.