I think Meloncov has hit the nail on the head. From your images, it looks like the surface normals of the polygons that make up your low-poly spheres are not being interpolated properly.
If you take a very low poly object and increase the poly count with subdivisions, the tool won’t really know that you are trying to make a sphere, it will simply guess at what the vertex normals should be, given the starting polygons. If the starting polygons are “flat” - ie. all the vertex normals of a given polygon are the same - then you will get a very poor result.
Even if your vertex normals are shared, and are taken from the sphere surface at that point on the sphere, if you have too few polygons, you will still get interpolation slope discontinuities along polygon edges. You simply can’t avoid that - unless, as Meloncov suggests, you map a normal map onto the polygons that overrides the normal interpolation.
Does that help?