Seems we are on the same page, albeit in different scales and with some symantics. I recall you are in the middle east and I am in the USofA.
Big multiple V-belts as one would find on a machine tool are called 'banded' or 'ganged' in my world. Also big V-belts can be had in 'matched sets' (matched for exact length, but separate belts.)
The little brother is called 'grooved' or 'ribbed' and in automotive speak is a 'serpentine' belt, although that desribes the arrangment and not the belt structure. A difference, (other than the obvious . . . size) is that the grooved belt has traction material on the smooth side which is intended as a drive surface in a serpentine arrangement.
I'm not clear on which belt type 'poly v' refers to, but it seems that you used the term for both a big machine tool and Hood's little engraving spindle, so it seems the term is somewhat universal. And yes, your are right about suppliers also. A 'grooved' belt purchased from an industrial supply house might be $10. But the identical 'Serpentine' belt from an automotive store is $38.
Go figure.