Female Downy Woodpecker, Louisville, Kentucky, 2021-05-01
The two main ways I know to distinguish a Downy from a Hairy Woodpecker are:
1. Look for black spots on the outer white tail feathers. You can see these in the photo. Only Downy's have the spots. If spots are missing, it may be either species.
2. Look at the size of the bill. Imagine it rotating 180 degrees, and check if it would extend past the eye. If it would, then it's probably a Hairy Woodpecker.
Personal instance for myself.