Oh watch out for those worms....
You will get many responses and unfortunately many of them will be information which has been provided by manufacturers and sellers who really don't understand.
First up, realise that 'polish' is a generic term and can mean anything from a cleanser that contains no abrasives and no protectants right the way through to heavy oil based formulations with multiple abrasives and fillers, waxes, silicones, polymers (etc.). Never trust a polish to be one thing in particular, often you can get the facts from the description but often you actually need to use the product (or read reviews) to ascertain exactly what it is. In the context of this topic, I am presuming you mean a 'polish' to be a water/oil or oil/water emulsion containing an abrasive but little else.
That in mind, your polish is going to remove all surface contamination that remains as well as abrasively remove oxidised or otherwise damaged paint. As a result, the paint is left looking 'shiney' because it is smooth and you have minimal defects which alter the reflection of light thus degrading the appearance. You should also note that this is frequently assisted by 'fillers' which do just that, fill small imperfections so that they are not visible. In practice it is extremely hard to produce a product which does zero filling.
Now the wax. Yes indeed, it will protect. However, it can also do things to the appearance. Optics relies on refractive indexes which basically define how fast light travels in any given material. Realise this is a bit of a simplification but waxes and the other ingredients have a different index to the clearcoat and of course to the air. At each of the interfaces (wax/air, wax/clearcoat, etc) there are reflections and the different refractive index changes how light is reflected. As you will appreciate, 'shine' is closely related. So yes, wax will protect but it can also alter the appearance. In addition, most waxes will now contain silicone oils and polymers and these will make an even more pronounced effect.
Last little note is that traditional sealants work rather similarly to wax - the high tech/nano ones really do not. Again to an approximation, they actually become part of the surface and rarely are thick enough to product a notable effect (think about it, light has a wavelength of several hundred nanometers whilst the coatings are often only a few nanometers thick). So with these products, you are absolutely bang on, the polish or more accurately the entire preparation process are what gives the shine whilst the top product genuinely seals that shine in place but does negligible little to alter it.
All the best
