I suppose I'll start off with an example of what confuses me.
When considering how magnetism arises from special relativity, one example is often used. Consider a wire at rest with net charge density 0, and an electron outside of the wire. Now run a current through the wire such that the electrons inside move at speed $v$, and move the electron outside at speed $v$ parallel to the wire. The electron outside will experience a magnetic force and begin to move. From the reference frame of the electron, however, the electrons within the wire are stationary and the protons are moving with velocity $-v$. Thus, the protons get contracted, and so the charge density of the wire increases, and so the electron outside experiences a force toward the wire.
I get confused at the "the protons get contracted" step. It seems like what is being described is that charge density increases because the space between the protons is getting contracted, not the protons themselves. But I've heard that moving bodies themselves get contracted due to length contraction.
Another example is that of a spaceship traveling towards a distant star at .5c. I have heard that from the frame of reference of the spaceship, the distance between the spaceship and and the star gets contracted. But from the spaceship's frame of reference, all it observes is a star moving towards it, and so should see the star contracted. Why is the space between the spaceship and the star getting contracted? The observer can't tell that space is moving, after all, right?
I guess more generally I'm confused about how length contraction applies in different reference frames, and on what it applies to.