As you increase distance from a sphere, its edge (in the case of the Earth, the horizon) covers more earth as it approaches the size of the entire circumference and your visual of the sphere approaches 50%. As with gaining distance from any object, the amount of FOV needed to see the 'entire' object decreases.
At roughly 1,200 miles (the border distance between Low-earth orbit and medium-earth orbit satellites) a Field of View of 103 degrees is required to see horizon to horizon. Fish eye lens typically see from 100 - 180 degrees of view.
This is the set-up. The camera is positioned roughly 1,200 miles from the Earth. And pictured is the 103 degree FOV camera which will see the entire horizon and therefore you can see the FOV is tangential to the Earth from the camera's position.

This is what the camera sees:

Replace that camera with a 35 mm (focal length) camera. Which has a FOV of about 50 degrees. This is the result:
