A pump is exactly that, a pump. I don't know the tech part but it is the fluids filling the muscle and has nothing to do with growth.
You can break down the muscle fibers and have them repair...hence growth and not have a pump to a large degree. It is a benefit to growth to add the sets that promote the pump at the end of your sets because it puts blood etc.. in the muscle for it's recovery n development food so to speak.
Ya know I can do one set and pump myself up but that has nothing to do with overload and the breaking down of tissue and the following repair as we rest.
There is a workout routine in that you build the muscle pump, full and then follow your ordinary routine subsequently during that session. Theory is to load up with the blood and nutrients before the break down.
When we get that pump, the big pump we think we have done much,,much more. But depending on how we achieve that pump is whether or not we've done more or a better workout.
I do a pump thing a lot for my psych after my sets are over.
My 2 cents