Downy Woodpeckers exhibit diversity in their head patterns. This variation allows observers to recognize individuals. The bird in the first photo caught my eye on 24 March 2017 because it seemed to lack the black line that runs from the bill to the shoulder on most Downys. As a result, this individual showed what appeared to be too much white on its head. Compare the first Downy with the one with a normal stripe in the second image taken on 1 January 2017.
The first Downy Woodpecker also sports a black line along the back of its head. Compare that pattern with the woodpecker in the final image, taken 27 February 2013. This difference in pattern is more common than the first. Clearly the books are mistaken that suggest this pattern difference is a way to tell Downy from Hairy woodpeckers.