Original: An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height above the Earth's surface because the Moon's gravity is weaker. Note that "height" in the common sense of the term can not be used for gravitational potential energy calculations when gravity is not assumed to be a constant.
Simplified: The Gravitational Potential Energy formula used here is only used when the objects are very near the surface of the Earth, because the acceleration must be the same during the change in height.