Here's a before and after photo that I hope will help illustrate the difference.
The bottom paddle was 'polished' using a rotary rock tumbler. The top paddle has been polished to a mirror like shine using polishing papers. To be fair, I don't think I polished the bottom paddle with a cloth or anything, so it's a little tarnished - but trust me, that's not the only difference.
Before I jump into using polishing papers, I'll give a little overview of tumble polishing.