A half moon
A horizontal half moon is called a crescent moon.
When you see a half moon, the position of the Sun is either directly to the right or left of the Moon as viewed from Earth. This is because a half moon occurs when the Sun, Earth, and Moon form a 90-degree angle, with the Sun illuminating half of the side facing Earth.
It is what ordinary people (not astronomers) usually call the "half Moon" phase. That describes it pretty well. We see exactly half of the Moon's Earth-facing side lit by the Sun. During first quarter the half that's illuminated is to the West.
When the right half of the moon is illuminated it would be called first quarter. (That's when you see the Moon from the northern hemisphere.)
Both the 1st Quarter moon and the 3rd (last) Quarter moon can be referred to as the "half moon" since we see half of the sunlit side of the moon.
No. When you see the whole sun-lit side, you call it a "Full Moon".
First or Third Quarter
A horizontal half moon is called a crescent moon.
This is when you can only see half a moon out at night.
Half-moon Half-Earth
Sunlight is always falling on the moon and illuminating exactly half of it. That doesn't change.However, we're usually not in a place where we can see the entire lighted half of the moon.When we do happen to be in a position to see it all, that's when we call it a "Full Moon".
The moon is only visible because of the sun's light, which is why the moon appears to glow. When there is a half moon, only half of the moon is reflecting off the sun's light. It all has to do with the angle of the moon, the sun, and the Earth, which is why the moon has so many different phases.
You often CAN see the "dark side of the Moon". It's easiest to do around the first quarter Moon or a day or two before that. The Sun shining on the Moon causes the Moon to reflect light, and we call this "moonlight". But if you were on the Moon and looking at the Earth, you could see the Earth by reflected sunlight, which we would call "earthlight". When we look at the first quarter Moon, we can often see the dark side of the Moon illuminated very slightly by reflected earthlight!
We see the Moon from different angles. When the Moon is opposite to the Sun in the sky, we see the illuminated part. When the Moon is in front of the Sun, we see the dark part. At a 90 degree angle, we see half of the Moon illuminated, and half dark.
The Moon orbits the Earth, while the Earth is orbiting the Sun. Because the Moon is moving, we see it in different positions relative to the Sun; we call this the "phases of the Moon". Only when the Moon is on the opposite side of the Earth from the Sun will we see a "full" moon.
The waxing moon phase is when the moon is transitioning from new moon to full moon, and the illuminated portion of the moon is growing larger each night. During this phase, we can see more than half of the moon's lighted side from Earth.
If you could see it, it would be a waxing half moon with the upper (eastern) half of the moon lit.