The main issue is that factory satin finish stainless guns are left with small machine marks from manufacture.
If you buy a factory bright polish gun, they use professional polishing equipment to remove the tiny marks and then bring it to a mirror shine.
While using metal polish and a cloth will bring a gun to as bright shine, metal polishes can't remove the fine machine marks nor bring the metal to a true mirror shine.
To do that you have to use fine abrasives to remove the marks and work down in grit until a metal polish can produce a true mirror shine.
Automotive stores sell extremely fine "wet or dry" abrasive cloth that can be used for this but be aware that it's extremely difficult to do this level of polishing without rounding off sharp edges, dishing out holes and leaving ripples in the flats.
Professional polishers have the specialized skills to do gun polishing without doing damage, and they use special shaped polishing tools to polish ares like inside the trigger guard, around frame features, and the cylinder flutes.
The quality of polishing is what sets a good blue job apart from a botched up mess. Gun polishers have years of experience and special equipment to do it whether on carbon or stainless steel.
So, if you want a bright and shiny gun, use metal polish and cloths.
If you want a factory level true mirror polish, it's going to require a lot more skilled effort and the risk of botching the gun are high.