This is how I always understood it. You have the Atlas Armlet and Earrings, which increase your attack power and magic power (i.e. physical damage and magical damage) and the Hero Ring which increases both. Now I've always wondered if equipping two Atlas Armlets or two Hero Rings has the same effect as two Earrings, but I've never tried.

The Hyper Wrist increases your Vigor, so all things associated with Vigor, not just physical damage, get a boost.