My guess would be both - it draws wall power up to a point and once it hits the limit of the charger (usually 5W for the small iPhone cubes) the rest comes out of the battery. So light use might still trickle the battery, but turning on the camera probably drains the battery slightly.

Not an expert, but I'm pretty sure it is drawing power from the wall. My understanding is it is not great for the battery to act as a pass-through for power.

Many cheaper devices warn you not to use the device while charging, because they don't invest in the circuitry to bypass the battery while plugged in.