Screenshot 1 is an image I use on my desktop. It has not been resized or touched up in any way. I loaded into Photoshop, cropped, then saved as .jpg.
Screenshot 2 is taken using the Snipping Tool on the desktop and you can see artifacts in it. This is exactly how it looks on my Windows 8 1680x1050 desktop, so further compression as you may think is not to blame.
The point is, Windows degrades images when it puts it on the desktop. That shouldn't be imho.