full moon
The crescent Moon implies a gibbous Earth, as seen from the Moon.
If you are standing on the full moon you would be facing the earth at night.
Any person on earth can see the phase of the moon by looking for the moon in the night sky. The only reason you would not be able to determine the phase of the moon by observational means would be if the night sky was obscured by clouds.
That would be the "Full Moon".
a waxing gibbous
Waning gibbous.
The New Moon
New Moon Phase
In the new Moon phase.
New Moon Phase
It would be the opposite. If we went to the moon when it was full, we would look back at an earth in shadow (a `new earth`) If we went to the moon when it was new, then it would be between us and the sun, so we would look back at a full earth. For a waxing gibbous from earth, the earth would be a waning crescent from the moon.
As seen from the moon, the Earth is a brighter source of light than the moon is as seen from the Earth. This also depends upon the phase of the Earth, just as the brightness of the moon varies by phase. A full moon and a full Earth are in the brightest phase.