He's showing off just a touch of his namesake belly color.
It's hard to see the subtle ring around the neck of the ring-necked duck, unless one is lying in your hands and its head is dangling lifelessly downward, exposing the full length of the neck. Red-bellied woodpeckers in their normal pattern of living, keep their bellies firmly propped against tree trunks, making any red feathers very hard to see. Again, on a bird in the hand, those red belly feathers pop right out at you.
I'm glad we're not still shooting birds to identify them. It's loud, bloody, hard to do, and too hard on the birds.