Different frames of reference use different coordinates. The speed of ligh measured with non-local coordinates can change. But in any frame, using local coordinates the speed of light is always the same.
The term 'rest frame' is not meaningless. If you are considering a scenario with many inertial observers you can nominate any one of these to be your rest frame. It makes no difference which one you choose, the physics is the same. So it is not meaningless, it is irrelevant.