Whether two clocks are synchronized or not is frame-dependent. If two rockets are traveling at constant velocity, and the clocks on the rockets are synchronized in the frame of the Earth, then they will not be synchronized in the frame of the rockets. Why is that?So in their co-moving frame the clocks undergo the same acceleration and thus the same deviation to the original time in the rest frame, but nevertheless they also develop an offset of time in between them (to an observer traveling along in the commoving frame). How is that possible?
Well, Einstein gave an operational definition of when two clocks are synchronized in a frame in which they are at rest: Send a light signal from the rear clock to the front clock, and back again. Then there are three relevant events: (1) the signal is sent from the rear clock, (2) the signal is received by the front clock and a reply is sent, (3) the reply reaches the rear clock. The clocks are synchronized if the time of the second event, as shown on the front clock, is halfway between the times of the first and third events.
If we apply Einstein's definition of synchronization to moving rockets, then we find that in the trip from the rear clock to the front clock, the light signal takes longer (according to the Earth's frame) than in the return trip. That's because the front rocket is moving away from the light signal, so it takes longer for the light signal to catch up, and the rear rocket is moving toward the light signal, so it takes less time for the light signal to catch up. So if the clocks in the two rockets are synchronized, according to Earth's frame, then the front clock will be ahead of the rear clock, according to the rocket's frame (that is, the time shown on the front clock will be more than half-way between the first and third events, as described above). If the clocks are synchronized in the Earth's frame, then there will be a positive offset of the front clock in the rocket frame. If the rockets are traveling at constant velocity, then this offset will be constant.
If instead of the rockets traveling at constant velocity, the rockets are accelerating, then the offset will keep growing with time. So the riders in the rocket will interpret this as the front clock getting more and more ahead of the rear clock.