Thank you. If the yardstick is light-speed, is there any meaningful distinction between saying that space itself changed and that there are local perturbations

Thank you. If the yardstick is light-speed, is there any meaningful distinction between saying that space itself changed and that there are local perturbations to the speed of light? The thing I struggle with is that we normally think of things occupying space. If space itself gets distorted, then the size of those things should change, too. Or is that mental model a useful but ultimately incorrect way to think about the world?