If you want to completely remove an old layer of wax use either Dawn or Spray Nine in water. Both products will effectively remove all the wax.
All waxes are a blend of different waxes cut in a solvent blend. The cleaner waxes are merely this same combination of waxes cut in a harsher solvent blend, which aides in greater cleaning power. The hardest wax has a higher concentrate of carnuba and gives you the best shine. However, it is also the most difficult to buff out. The primary difference between a wax and a polymer coating is the wax is thermoplastic and the polymer is thermoset, for all intent and purposes. This simply means that the wax will soften up as the temperature increases whereas the polymer will not.
When you apply any wax over a previous layer of wax the solvent blend will dissolve the old layer. If you want to prove this point, apply wax to a small area and don't buff it out. Come back the following day and apply a second coat of wax over the previous layer and the second coat will dissolve the first coat. Therefore, applying multiple coats of wax is pointless, since you're left with the same thin coat of wax. Each subsequent coat of wax will dissolve the previous coat. This does not apply to a polymer coating. Multiple layers can be built up to give a higher refractive index and greater shine.
The principle behind a wax shine is leaving a very thin layer of wax on the surface. When you buff the dried wax either by hand or machine, you remove most of the wax. This is done because you're generating heat and removing most of the wax. You can see this same phenomenon when you buff an apple.
The thermoplastic properties of a wax contribute to it softening up as the temperature rises. When this happens, it picks up and retains contaminates which contribute to it becoming dull. If the wax contains a high percentage of carnuba wax it will retain it's shine for a longer period of time, due to it's higher melting point. That's also why waxes with a high level of carnuba are more difficult to apply. They require more heat/friction to melt.
The polymer coatings such as Zaino, Rejex, Pro Polish, etc. thermoset after a period of time-like 24 hrs. Subsequent coats can be built up to afford more protection to the surface and a higher level of shine.
Unless your hull is heavily oxidized, you can forget about the compounding and polishing steps and use either a wax or polymer.