Here's the breakdown:
* Apparent Motion: From our perspective on Earth, almost all stars appear to move across the sky throughout the night due to the Earth's rotation. This is like watching a carousel – the horses seem to go in a circle, but it's really the platform we're standing on that's rotating.
* Actual Motion: Stars are not stationary in space. They move relative to each other and to the Sun, but these motions are much slower than the Earth's rotation. We don't notice these motions easily because they take thousands or even millions of years to be noticeable to the naked eye.
So, to answer your question directly:
* Do all stars move in the sky? Yes, they appear to move because of the Earth's rotation.
* Do all stars actually move in space? Yes, they do, but these motions are very slow and not easily noticeable.
Let me know if you have any other space questions!