Is there a difference between the side window glass in a 1970 Pontiac GTO coupe and the convertible.
I do not think so. Body parts are usually the same based on the base car model.
The attached picture makes me think the shop has installed the wrong window.
It is probably the right window but you need to pull the interior panel and make adjustments to the hardware that hols it in place. There are typically multiple adjustments to get it sealed correctly. Up, down, in , out all have screw/nut fastners that will need to be played with.