Stars are known to move around the poles, and also have their known Proper Motion. But it is often said the stars are fixed in comparison to the planets which rotate. It is the earth that is moving primarily which gives the illusion that the stars move also.
Yes, the stars move. Yet, because of their great distance, the motion across a small arc of sky must be measured in centuries or millennia.
The relative velocities of stars are on the order of tens of kilometers per second, but because stars are many trillions of kilometers distant, it could take centuries or millennia for any star to move 1 degree of arc, even if within a few light years.
The motion of all the visible stars in our night sky is one of orbiting the hub of our Milky Way galaxy. Not all follow the same path, so some are passing while others are being passed.
Scientists measure the motion relative to Earth as "proper motion" (delta Right Ascension and delta Declination) and "radial velocity" (toward or away from Earth. With these, you can calculate +/- XYZ vectors.
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