The pattern that determines the day and night side of Earth and of the Moon depends on their motion and exposure to the Sun.
Explanation:
The Earth and the Moon and both objects that do not produce their own light, but instead they receive light and reflect it. The light comes from their central star, in this case the Sun. Both of these bodies have their own motions, and those motions determine the day and night patterns.
The Earth spins around its own axis, which makes every part of the planet exposed to the Sun during a period of roughly 24 hours. This motion on its own will make the day and night patterns the same all year round though, but its not like that. The Earth has a tilt, and this tilting makes one of part of the planet more exposed to the Sun in half of the year, than the other. That in turn makes the days longer in the part that is tilted toward the Sun, while the nights are shorter, and vice versa.
The Moon doesn't have tilting, so its day and night patterns depend on its position in respect to the Sun and the Earth. If the Earth is between the Moon and the Sun, all of the Moon experiences night. If the Moon is not in the shade of the Earth, than half of it experiences day and half of it experiences night, which have roughly the same lasting throughout the year.
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