I was using CreateWindowEx() with the WS_EX_OVERLAPPEDWINDOW style. In Windows 7 this produced a nice looking border when the window was restored and no border when the window was maximized. In Windows 10 I can see no real difference between using the flag and using a ZERO for the flag when the window is RESTORED. However, when the window is MAXIMIZED, Windows 10 apparently reserves the SPACE for a border but never actually DRAWS anything in it, resulting in a narrow frame of "bleed through" from whatever is behind the maximized window.
The solution is to not use the the WS_EX_OVERLAPPEDWINDOW flag in Windows 10 because the implementation of it is somewhat broken.
Thanks helping me to realize what Microsoft has broken!