In Traditional Wicca, Drawing Down the Moon is done by the High Priest evoking the Goddess into the High Priestess so that she becomes a vessel containing the Deity. The Goddess can then speak through her lips and act through her body.
Alternatively, the High Priestess can perform a Drawing Down of the Sun, in which she evokes the God into the High Priest and he then becomes a vessel for the God.
It is extremely rare (although not unknown) for the Draw Down to result in the God being drawn into the Priestess or the Goddess being drawn into the High Priest.
Drawing Down the Moon and Drawing Down the Sun are essentially equal in power and effect, the only difference being which Divinity is being drawn down into which person, High Priestess or High Priest.