quarter moon
This is the first quarter phase. The moon looks half lit, half in shadow, but you actually can only see one quarter of the moons surface at this point (during a full moon, you would only be able to see half of the moons surface - the half that faces us).
That phase is called the third quarter or it could be called a waning half moon.
half moon
The waning Moon phase in which only one-half of the lighted side of the Moon can be seen from Earth is called the Third Quarter Moon. It occurs when the Moon has completed three-quarters of its 29.5-day cycle.
This is what causes the so-called "phases" of the moon: although fully half of the moon is lighted, we can only see part of the lighted part. A person on earth hardly ever sees all of the lighted side of the moon. When he does, he calls the sight a "full moon."
Those shapes, and the corresponding phases, are called "crescents" ... when the lighted part that we see is less than half of a full disk.
Last quarter.
The Earth only has one natural moon, called the Moon. Earth does not have three moons.
If you see two moons, either you are no longer on planet Earth (which has only one moon) or you are suffering from double vision.
One half of the moon, the side that faces the Sun, is always lighted. But we usually see only part of the lighted side (phases) as the Moon orbits the Earth. When the Moon is directly between the Earth and the Sun (a new moon) none of the lighted side, facing the Sun, is visible from Earth.
Because the earth relies on the light from the sun. Only half of the planet can be lit at any time - due to the fact that light travels in straight lines.
Only one so it's called The Moon.