@layman,
I will elaborate slightly. In the H-K experiment 3 different clocks were compared.
1. One remained stationary, relative to the earth's surface, at a Naval Observatory Station in Maryland.
2. One flew east at the relative rate of of 500 miles per hour, completely around the world, until it landed back in Maryland.
3. The third clock did the same as 2, except it flew west.
When all three clocks were back in Maryland, they all showed a different amount of elapsed time.
If you had tried to predict their readings, using the base as a reference point, your predictions would have been wrong.
If you had tried to predict their readings, using the east-bound plane as a reference point, your predictions would have been wrong.
If you had tried to predict their readings, using the west-bound plane as a reference point, your predictions would have been wrong.
When I say "predict" I mean if you used SR as your theoretical basis for making the predictions.