The Moon is - centre to centre - 384,403 kilometers away.
Mars on the other hand:
Mars on the other hand:
It gets more complicated than this; however, because both Earth and Mars travel in elliptical orbits around the Sun. Their orbits can bring them close or more distant to each other depending on what point of their orbit they're on.
The closest theoretical point Earth and Mars can be is when Earth is at its aphelion (or most distant point in its orbit), and Mars is at its closest. At this point, the two planets are separated by only 54.6 million km.
This is theoretical though, and would take millions of years to get the perfect point where the planets lined up. The closest point in recent memory was back in 2003, when Earth and Mars were separated by only 55 million km.
The furthest theoretical point is when Earth and Mars are on opposite sides of the Sun, and both at their furthest point from the Sun. At this point, the two planets can be 401 million km.