One correction: "moving" has nothing to do with it, crossing world lines does. Space ship flying at the speed of light (well, close to it) is also following its world line, so its clock is not "worse" or "better" than the one on the Earth. They both show "proper" time (https://en.wikipedia.org/wiki/Proper_time). When the ship starts to accelerate that's when its time becomes skewed. Also times at two different points of space are not comparable as there is no way to synchronize them, it depends on observer's speed. So "all clocks that are at rest" _always_ show different time if they are not at the same spot (well, they may show "the same" time like a stopped clock shows correct time two times a day).