Historically Americans came from Old English, but beyond that, Americans usually vary more because most are bred for fighting, not show, thus you have different named lines and most of them are squirrel tailed or with tails carried somewhere between 50-90 degrees above horizontal.
American Games are found with a much closer dubbing in males, beyond that it is a bit hard to say any true differences because they do vary. There are different leg colors, comb types, body shapes/carriage, tail expansions, etc.
So in a nutshell, American Games are basically a large group of birds very similar and originating from Old English, but many Americans are still bred more for fighting purposes than show. With that in mind, they vary, especially according to their lineage.