In the options from pivot point, is the option 'Bounding Box center' the same as the option 'median point'?
for the second question :
the bounding box center is not the same as median center :
-The Median center is calculated as the average of all selected points ( vertices or object centers ) so it depends on the density distribution of the mesh
-The bounding box : is the smallest box (Cube ) that can contain the mesh of an object while aligned to the local space
-The bounding Box center will always be at the center of this bounding box regardless of the density distribution of the mesh inside