During a full Moon, the Moon is opposite the Sun in the sky. That's why we can see the full face of the Moon reflecting sunlight. As the Earth rotates, the Moon rises just as the Sun sets, but just on that one day of the month.
The stars are nowhere near as bright as the blue sky during the day, but the moon is approximately as bright in reflected sunlight as the sky during the day, and that's why we can see the moon during the day, but not the stars during the day," O'Meara said.