The Downy woodpecker is a very small (6 1/2") black and white woodpecker, male has a red patch on the back of his head. It visits bird feeders regularly in winter time.

The Hairy woodpecker is almost identical to Downy except it is larger (7 1/2 - 9 1/2") with proportionally longer beak and no black marks on white outer tail feathers. The last two potos are Hairy woodpecker, as you can see it lacks the black markings on its tail.