Why Do They Call It A Red-bellied Woodpecker?

People that aren't specifically into birding sometimes refer to a Red-bellied Woodpecker as a Red-headed Woodpecker which is a  different species. It is understandable because the Red-bellied Woodpecker does have a lot of red on the top of it's head but where is the red on the belly?

Unfortunately, back in the Audubon days they had to shoot the bird if they wanted a close-up look at them. Otherwise, they probably would have came up with a different name. See that little splash of blush color on the underside? Apparently, that is supposed to be the red belly!