Those shapes, and the corresponding phases, are called "crescents" ...
when the lighted part that we see is less than half of a full disk.
crescent
The crescent phase.
A waxing crescent is the phase of the moon where only a small sliver of the moon is illuminated on the right side. It occurs just after the new moon phase and is characterized by the increasing visibility of the moon.
As of February 5th, 2010, the moon will enter the Last Quarter, and will enter the New Moon phase as of February 14th. So on February 13th, the moon will still be in the Last Quarter phase.
When the sky is clear but still only a small part of the moon is visible, the cause may be any one of the following: -- The moon is in its waning crescent phase, during the last 6 or 7 days before New Moon. -- The moon is in its waxing crescent phase, during the first 6 or 7 days after New Moon. -- An umbral lunar eclipse is in progress.
The phase of the moon that immediately precedes the new moon is the waning crescent. During this phase, the moon appears as a thin crescent shape, with only a small portion of its surface illuminated by the sun. As it continues to wane, it moves closer to the new moon phase, when it becomes completely dark and is not visible from Earth.
Last Friday, it was a waning crescent moon, with only a small sliver of the moon visible in the sky before sunrise.
When the sky is clear but still only a small part of the moon is visible, the cause may be any one of the following: -- The moon is in its waning crescent phase, during the last 6 or 7 days before New Moon. -- The moon is in its waxing crescent phase, during the first 6 or 7 days after New Moon. -- An umbral lunar eclipse is in progress.
Only during a full moon.
The two phases of the moon that appear as only a tiny silver crescent are the waxing crescent and the waning crescent. During the waxing crescent phase, the moon is transitioning from new to first quarter, and a small sliver of light is visible. Conversely, the waning crescent phase occurs after the last quarter, with only a small portion of the moon illuminated before it returns to the new moon phase. Both phases create a delicate, thin crescent shape in the night sky.
A Lunar eclipse occurs only when the moon is in its full moon phase.
That is called a "thin crescent moon." This phase occurs when the illuminated portion of the moon is only a small sliver, making it difficult to see in the sky.