Downy woodpecker

One way to separate male Downy and Hairy woodpeckers is the tail and nape. Almost all Downy woodpeckers (male and female) have black horizontal bars on the outer white tail feathers--there can always exceptions, so I won't say all. Male Hairy woodpeckers also usually have a black stripe running down the middle of the red on the nape, which Downy woodpeckers lack.

Done