The difference is the distance the light reflected from the moon has to bridge across the Earth's atmosphere.
The closer the moon is to the horizon, the longer the distance the light has to traverse the Earth's atmosphere, and the more of the blue spectrum is lost (while the red spectrum gets through untouched). So, the color of the moon will appear closer to red, the closer it is to the horizon.
During the day, the same is true, but on top of that, the direct sunlight also has an influence, making the moon seem almost white.
