The "gibbous" moon phases occur when the Moon is more than half illuminated, but less than full.
waxing gibous
Waxing crescent
A waxing crescent.
Waxing Gibbous
Waxing crescent.
The phase that occurs between the first quarter and the full moon is the waxing gibbous phase. During this phase, the illuminated portion of the moon is increasing in size, moving towards the full moon phase.
The waxing crescent moon phase occurs between New Moon and First Quarter.
A waxing crescent phase occurs in the moon's cycle when the illuminated portion is increasing but less than half. This phase is visible in the western sky after sunset. It is a transitional phase between a new moon and first quarter moon.
A first quarter moon occurs when half of the moon's face is illuminated, appearing as a right half-circle. A waxing crescent moon occurs when only a small sliver of the moon's face is illuminated on the right side. The first quarter moon is the halfway point between the new moon and the full moon, while the waxing crescent occurs in the earlier stages of the moon's waxing phase.
it occurs after the first quarter
Prophase
The Moon's third quarter phase, also known as the last quarter, occurs when half of the Moon's visible surface is illuminated and is located between the full moon and the new moon. The first quarter phase, conversely, also features half of the Moon illuminated but occurs between the new moon and the full moon. Both phases showcase the same amount of illumination (50% of the lunar surface), but they are opposite each other in the lunar cycle, with the first quarter appearing in the evening sky and the third quarter in the morning sky.