Man, I think were getting carried away with terms here.
To me, an abrasive polish is a product which contains minuscule granuals of material meant to abrade away any surface debris or imperfections. This is what I know as an abrasive polish.
On the other side of the coin are what I call cleaner polishes, such as DG 105/101. Neither contain (from what I understand) abrasive polish products, but do contain chemical cleaners. I dont really think using a paint cleaner "polishes" paint. It just cleans it, which removes surface contamination only. When using a chemical cleaner, the actual polishing comes from the attrition associated with the applicator used to apply.
As for the correlation with acid, the acid isnt really abrading, its dissolving. Abrading takes a physical force, where as dissolving is purely chemical.