The method does not necessarily change, however the product typically does. I like to add all LSPs by hand and usually favor paste waxes. Everyone has their own individual favorite products for different colored vehicles as well as their desired results whether it be liquidity and depth or shine and wetness. Personally I like Souveran on darker paints, TS on darker metallics, Natty's on lighter metallics, and Signature on white and silver but to each their own. Basically it comes down to you playing around with different combos on different colors to see what suits your taste better.
The pads however are more easily explained. Polishing pads exhibit the ability to clean surface contaminants because of their porous structure and increased firmness. The finishing pad lacks cleaning ability because of a finer pore structure; they are also softer as compared to polishing and compounding pads. IMO you need both.