The Difference Between "Polishing" and "Buffing"
"Polishing" a piece of metal removes a moderate amount of metal from the piece, using coarse to medium abrasives in stages. The piece will have a "brushed" look and you will not be able to see any reflections in it. Polishing removes scratches and minor surface imperfections which are too deep for buffing compounds to remove efficiently. If you run your fingernail over a scratch and it gets caught, then the piece should be polished before buffing. The key to success in polishing is to remove just enough material to make the surface even and no more.
"Buffing" removes very small surface irregularities and makes the surface almost perfectly smooth by removing a very small amount of metal. Just like polishing, buffing is done in stages from coarse to fine. Buffing compound grits are so fine that you might not be able to tell the difference between compounds by rubbing some between your fingers. Their difference in performance, however, is significant.