Q: Screenshots double the Size

My screen shows a 800px image on a 3008px resolution monitor.

It should fit 3.75 times about.

It does fit about 7.5 times over it

I took a screenshot, and that screenshot is then 6016px in with. So why does OS X handle the monitor as 6016 px, and not 3008px?

PS and LR are probably doing everything right then, just the monitor gets interpreted as 200%. In the setting it says clearyl 3008px, and the screenshot is exact 6016px wide.

Any solution for this?