I am studying special relativity but it isn't making any sense. I know that if I have space time co-ordinates in a stationary reference frame I need to use the Lorentz transformations to get the co-ordinates in a moving reference frame but I don't understand what this actually means physically and how to decide which clocks to apply the transformations to.
For example, two clocks are distant and synchronized. Clock A is stationary and clock B is moving fast towards clock A. The moment they pass an observer who travelled with clock B can see both clocks and sees clock A is slow and clock B is fast but an observer who stayed with clock A sees the opposite even though they are in the same place looking at the same pair of clocks at the same time? The clocks really physically read different values depending on which observer is looking?
Edit: I know acceleration changes things, so please assume clock B was always moving at a steady speed and the clocks synchronized with a flashing light source that was exactly half way between the clocks at the start of the experiment.