Mileage in extraterrestrial vehicles - Moon and Mars distances

I recently run into a cool infographic showing distances driven by vehicles on the surface of the Moon and Mars, and a great time-lapse of the martian rover Curiosity - its 9 month squeezed into a minute.
That’s all dandy, but one has to get to the Moon and Mars before being able to enjoy some offroading. How far are they? The answer is not one number.
In this post: distances to ponder.

Earth, Mars and Moon to scale   --   source: ESA

Moon Phases & Faces

Why do we see the Moon changing shape on the night sky? Why do we see only one side of the Moon, and what's up with that "dark side"?

Lunar Phases

This will be a little visualization exercise.
Imagine that you are above the North Pole looking down on the Earth and the Moon orbiting around it. The Sun, shining from your right, illuminates the half of the Moon that faces it, this is the day side of the Moon.
From the Earth, we see the Moon changing shape: as the Moon revolves around the Earth, we see varying amounts of its sunlit day side and dark night side. This causes the lunar phases.