Yes, the moon is closer. On average it is 1,000 times closer than mars but you only need about 2.3X the rocket power (DeltaV: Moon: 2,635m/s vs Mars: 6,268m/s ) to get there compared to the moon.
But they are both far enough away that is doesn't really matter.
A colony in either place cannot rely on outside assistance to come and help them.