Polishes and compounds cannot be compared to sanding with abrasives as they each have their own functionality. The former is known as "Chemical" abrasion" while the other "mechanical"
In fact, the more I think about it (and it took some thinking) your question is more about stepping up through different levels of polishes (with each working at a removing a specific grit of scratch) without even using any mechanical abrasion. This in hopes of producing this uber mirror like shine. Is that correct?
But every polish and compound has as it's basis the target of removing a certain defects introduced into the finish by mechanical abrasion.