The 4K standard is 3140 x 2860 pixels which works out to 8.2 Megapixels.
Phantom sill shots are 4000 x 3000 pixels which works out to 14 Megapixels. So, still shots have a higher resolution than 4K video.
Video is generally more forgiving. You don't see flaws in moving images as readily as you do stills.
I don't see any noise in your examples. Noise is a grainy effect that is introduced to an image. Go to this link and scroll half way down. -->
A Beginner's Guide to Photography - Part 1 - Intro and ISO There is an example image showing noise at different ISO levels. The higher the ISO you use, the more noise.
It appears that your cropped image above is 'unsharp'. There is a slight blur present. This could be from motion blur, but I suspect it's just the limits of the lens and the sensor.
Zooming in 100% with still images will bring out any flaws or lack of sharpness in a lens. This is normal.
The more you zoom, the more unsharp it will be. If you crop out a small area of a large image, it will never look as good as the whole image shrunk down to fit the average computer screen.
There are editing techniques that allow you to sharpen images.
Sharpen Images In Photoshop With The High Pass Filter That will render better results. Post processing still images is a science unto itself. There are many forums dedicated to it.