From one day to the next, the view of the Moon would change very differently for an observer on Mars than for an observer on Earth. The phase of the Moon as seen from Mars would not change much from day to day; it would match the phase of the Earth, and would only gradually change as both Earth and Moon move in their orbits around the Sun. On the other hand, an observer on Mars would see the Moon rotate, with the same period as its orbital period, and would see far side features that can never be seen from Earth.