Essential difference between electrostatic shielding by a conducting shell and magnetostatic shielding is due to

Electrostatic shielding is a situation in which the effects of electric field are choked for both the external and internal content. A conducting shell obstructs the effect of external electric field on the contents of the interior whereas the same is also applied for the internal content which as not connection with the external environment.

In case of Magnetostatic Shielding, the object is kept in a cage or barrier made up of high permeability magnetic substance to cease the effect of external magnetic field on the object or to constrict the effect of a magnetic field on the external environment. Unlike the electric shielding, the magnetic field is not completely blocked but passes around the enclosure. Hence, we can only lower the influence of the magnetic field by placing high permeability materials.