I'm not quite sure what question you're asking, but both terms refer to the leading edge being curved downwards, with "droop" being permanent and "droop flap" being a hinged device, like flaps, except on the leading edge. These devices increase Clmax only by preventing the stall until a higher AoA, unlike trailing edge flaps, which have an increased Clmax at a lower AoA. The higher AoA of the stall for leading edge devices isn't that useful when used alone, because flying at such a high AoA is very awkward, if not impossible. Combining them with trailing edge flaps is ideal, because trailing edge flaps lower the required AoA at every airspeed.
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