Is the smoothing option meaningless since the displacement map is meant to be extracted from high polygons?
So what is the correct way to create a greyscale bump map?
And here is my blend file
Blender Stack Exchange is a question and answer site for people who use Blender to create 3D graphics, animations, or games. It only takes a minute to sign up.Sign up to join this community
Now it's much more clear and you put your "real" question.
It seems you wish to bake displacement (ie: geometry) from shading (ie lighting): it will never work imho.
Use a real "smoothing" option, like more subsurf
so, why "Shade Smooth" doesn't work when baking a displacement map, unlike the "normal map" (that works)?
because "smooth shading" is, in fact, just a shading trick: it alters the normals, to let the object appear smooth (as if it had more geometry, which it has not), so the normal baking takes it into account.
the "displacement baking" instead needs to bake the geometry "height levels" into color levels (the baked image), but since "smooth shading" leaves the geometry untouched, you get the same identical result as without the smooth shading...