They all do the same thing when it comes to cooling a horse after exercise. They trap a layer of air that keeps the horse warm and wick away moisture. This stops the horse getting cold when they cool down and they are wet with sweat.
The old sort of sweat rug looks like a string vest. The modern sort are fleece or other technical fabric.
Fleece coolers and other non 'string vest' sorts can be used to keep the horse clean in lue of a stable rug in he summer or for coldbloods in the winter.
They can be used as an under rug to keep your turnout clean or used over a stable rug to keep that clean! They are easy to pop in the wash and dry in no time.
A fleece or thermatex type rug could also be used as a travel rug.