Spotted belly and thick black band on the outer edge of the tail.
Blue wings, strong black band again. Male American Kestrels.
Streaky belly, only a thin black band on the edge of the tail: female American Kestrels. The topside of her wings are also reddish, but we can’t see this from below.
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This work by Matthew Wills is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Backyard and Beyond 
Good ID tips. You don’t always get to see the top of the bird. This is the species that started my birding addiction. It will always be on the top of my favorite bird list. They are beautiful powerful, graceful, fast and extremely adaptable to changing conditions. I expect we will be seeing them for the long haul.
Sure hope so.