The problem is a matter of terminology. In the Adam's Polishes ecosystem the term "polish" refers to an abrasive product that, when used with a machine polisher, actually removes a tiny bit of clear coat in order to level, clean and shine the painted surface. It does not (generally) include protection. Just removes defects from the clear coat.
Protection in generally added after polishing in the way of sealants, waxes and coatings. This is in order to protect the just corrected paint and help the paint stay nice longer.
The problem is that many other products are billed as "polish" when they are not really removing any blemishes. They are just shining up the existing surface.
I'm not discounting the satisfaction you have with that other product - I'm just trying to clear up the terminology used with Adam's products.
I started out years ago with Zaino products and it was never clear to me what product was doing what. I switched to Adam's because the whole line just made more sense to me.
If you watch all of the Adam's videos you will get a real nice idea of what the products do and how they fit into an overall detailing plan.