I think the idea is to start with the lower resolution sphere (at the appropriate scale to print individual parts).
From this base sphere, mark the seams you want (seams will be useful to cut it later).
For instance here all edges are marked except for the poles:
Now use the subdivision surface modifier and apply it. The modifier will subdivide but let the seams in place:
Now select an edge marked with the seams, then in the select menu, go to 'select similar' and choose 'seam'.
Now split the parts using the edge menu, then 'edge split'.
Select all. Extrude E but stay in place.
Scale down (still having the extrusion selected) to 0.9, for instance.
The selection is still there. Create a vertex group and call it 'inner'.
Invert the selection, and create another group called 'outer'.
Use and apply the displacement you want, using the 'outer' vertex group on the displacement modifier.
In edit mode, select all again. Then P and 'by loose parts'.
You may be ready for a 3D puzzle...