Three surfaces answer different questions
A sphere assigns one radius to every direction. That makes it useful for a horizon, shadow or great-circle calculation when a mean-radius approximation suits the task. It does not describe every surveyed height.
An oblate ellipsoid has a larger equatorial than polar radius. The WGS 84 reference ellipsoid has equatorial radius 6,378.137 km and flattening 1/298.257223563. Its polar radius is about 6,356.752 km, a difference of about 21.385 km.
Sea level and the geoid
The geoid follows gravitational potential and approximates undisturbed global mean sea level extended beneath the continents. Mass distribution makes it depart from a smooth ellipsoid. Mountains, trenches, waves and the geoid are different surfaces.
Compare predictions that share inputs
A photograph alone mixes geometry with camera projection. Combine measured horizon changes with height, noon shadows at several sites, celestial-pole altitude and long-distance routes. Each observation tests a different relationship; the same model must account for all of them.