No. The Moon is in orbit around the Earth and both the Earth and Mars are in orbit around the sun. The Moon varies between 360,000 and 400,000 km away and the closest Mars gets to us is 54,600,000 kilometers. Those numbers are a bit of an exaggeration because how much fuel you need is just as important as absolute distance/time to travel and for that you need 4 km/s of delta-v to get from Earth orbit to Moon orbit and 5.7 km/s to get to Mars orbit.
I meant that the Earth is closer to Mars than the Moon is, not that Mars is closer to Earth than the Moon is (of course it isn't, that would make for a big, big blood moon)
