I needed clarification as to two aspects of time dilation which seem distinct for me.
Consider an observer inside an accelerated rocket and another observer outside of it. The outside observer will perceive the time for the observer in the moving rocket as running slower, because of time dilation due to relative motion.
However, inside the ship, there will also be time dilation because of its acceleration (as it would happen in a gravitational field). However, this second aspect of time dilation will only happen inside the accelerated environment, and it won't affect outside observers (because they are not subjected to the same acceleration). Is that generally correct?
As explained here by Feynman, clocks at the bottom of the spaceship will run slower than clocks at the top. However, this particular time dilation doesn't affect observers outside of the ship. Outside observers might perceive both clocks running differently, but it doesn't affect their own. Is that correct?