In general relativity, space and time are mixed into a single geometry of spacetime. if you have taken high school algebra, this is analogous to the way that the x axis and y axis are mixed to produce the geometry of the plane.
Motion, in this scheme, *roughly* corresponds to a rotation of the axes, so the new axes no longer align with the old ones. That means that points that are 'simultaneous' (having the same x coordinate) in one need not be in the other (in fact, it is quite unlikely).
But notice that *both* coordinate systems see the other as having things wrong in similar ways. This is the origin of the 'twin paradox'. When two things are in motion, each one sees the clocks of the other as going slower.