Let me ed-u-ma-cate you.
1st Quarter vs. 3rd Quarter
The 1st Quarter is waxing, while 3rd Quarter is waning. This is because the 1st Quarter is rotating into a full moon, and the other is going away. Another way to differentiate the 1st and 3rd Quarters is to draw a picture. The 1st Quarter always has light on the right, and the 3rd Quarter always has light on the left.
Why do astronauts see the moon differently?
On earth, the illusion of the moon changing sizes are only shadows. On earth, if the moon was between the sun and the earth, it would be a new moon and it would seemingly disappear. But in space, it would look dark on the side facing the earth and light on the other. It would always look the same way from space, but on earth we get phases.