I own a docking station, capable of 4k 30hz, 1080p 120hz, but it only offers 800p 60hz. Why is 800p capped at 60hz and not 120hz if 1080p can provide it? If I upgrade to a 4k 60hz docking station, would I get 800p 120hz?

I pray on a 4K TV but 800p looks good enough and good framerate, I just would like more hz because my TV is 120hz and indie/old games should be playable at over 60hz