Object space:


The sculpt can be "re-angled" by the orientation of the object that it was paired with.
Tangent Space:

The direction the blendShape target gets applied in depends on the shape of the mesh. It kind of gets re-oriented to be "tangent" to the surface.
Both of them have really niche uses, and in 3+ years of professional rigging I have never used either of them, the normal blendShape mode is just fine. The tangent-space does have the advantage of being able to apply corrections after a spacial deformer like a lattice or wire, since it would come at the end of the deformation order, but that is rarely needed.
Hope that helped