Not even thousands of years, MW! Nearby stars move in the sky enough that, even though we can't tell by the naked eye, our telescopes can make pretty precise measurements. This is called proper motion.
The other effect is that nearby stars will move back and forth in the sky, relative to stars behind them, as the Earth moves around the Sun. This is called parallax. It's a pretty simple geometric effect: try putting your finger a foot in front of your face and closing one eye. Then close that eye and open the other one. Look at your finger. See how it moved? Then close that eye and open the first one again. The finger is back in it's original place. That's the same thing that happens when the Earth moves from one place in its orbit (your left eye) to another, on the other side of the Sun (your right eye), nearby stars move relative to faraway stars.