Will the resolution or the aspect ratio be different if I take a 500x500px screen-capture or screencap when I am using a Retina Display compared to a standard HD screen?
Screenshots on Retina Macs are exactly what you may expect: They're double the resolution and pixel density of non-Retina Macs. For a Retina MacBook Pro, full screen grabs are 2880×1800, with the pixel dimensions of elements double the size.
When overlaid with a screenshot of a non-Retina Mac, so that they're both the same physical size, the elements on the screen are the same size and position.
It's worth noting the difference of points and pixels on Retina Macs and Retina iOS devices:
On a standard-resolution device screen, one point equals one pixel, but other resolutions might dictate a different relationship. On a Retina display, for example, one point equals two pixels.
All Macs and iOS devices have a square pixel aspect ratio. Mac and iOS devices have different display aspect ratios though (for example, the iPad is 4:3 and a lot of Macs are 16:10).