The Sun and moon both have angles of about half a degree in our sky. Varies slightly with sun-earth, moon-earth distances.
I think what Public heel was trying to say was that to be a truly full moon (not even the tiniest portion un-illuminated), you would have to be exactly between the sun and moon (eclipse). This would be for a point source (which the sun is not). Since the sun has size you could move around from a postition exactly between the sun and moon and still see the moon as completely illuminated. Not sure offhand what the distance would be.
That is true for the moon's shadow. It is quite small, and the moon's umbra (the cone of shadow in which no part of the sun can be seen) barely touches the earth, sometimes not at all when the apparent size of the sun is larger than that of the moon.
At a total lunar eclipse the moon is engulfed by the earth's umbra. (The moon still can be seen because of stray light from the earth's atmosphere).