Why? As Henning alluded, it's the difference in angle of the airflow relative to the leading of the wing at stall when the flaps are down. Remember, AOA is defined relative to the chord line of the wing, which runs from leading edge to trailing edge. When you lower the flaps the trailing edge drops, and the AOA increases compared to the AOA with the flaps up even though the angle of the airflow with respect to the leading edge has not changed.
When that change is big enough, you need a second stall vane calibrated to the stalling angle with flaps down in order for each vane to provide the appropriate amount of warning prior to stall. If the only vane was set for clean stall, you'd hit the dirty stall before it triggered. If the only vane was set for dirty stall, it would go off way, way before you even got close to a stall when clean. For a C-172 or something like that, the difference isn't enough to matter very much, but with a light twin with a clean wing (like the Beech TravelAir or Grumman Cougar), it's big enough to be significant.
