* Waxing Gibbous: This is the phase after the first quarter moon, when the illuminated portion of the moon is increasing and becoming more full.
* Waning Gibbous: This is the phase after the full moon, when the illuminated portion of the moon is decreasing and becoming less full.
The difference between the two is whether the moon is getting "fatter" (waxing) or "thinner" (waning) before or after the full moon.