Kind of interesting about Flitz. When I saw sonicus' post saying Flitz was non-abrasive, I thought must have been a mis-read. Polishes have to be abrasive to work (they scratch off the oxidized surface of the metal).
Googled it a bit, and it's interesting that the company that makes Flitz claims that it's non-abrasive, but if you look at the safety sheet for Flitz paste (required for chemicals), the primary agent is aluminum oxide which is an abrasive. Strange that they would market it as non-abrasive, because it's just not true.
The differences in polishes is how fine the abrasive particles are. Rougher particles can cut through oxidation quicker but leave visible scratches. Fine cuts wouldn't be able to polish out deep scratches but leave a mirror-like finish. So, I'm sure Flitz is suffering from some hyperbole here - they have a fine cut of alumina so you don't see scratches.
You could have a purely chemical polish, but it's unlikely you'd have a mirror-like finish on metal after using it.
David Fung