I've seen the explanation before that holes are basically electron deficiencies in an atom and that the hole "moves around" by electrons from surrounding atoms shuffling to fill that spot which is a very spatial way of viewing what a hole is. However, when I think about the band structure picture, the excitation of an electron from the valence band to the conduction band leaves behind an empty spot in the valence band hence being the "hole" but that's just a momentum space picture.
What's the connection and which one is more correct? How can I reconcile the bandstructure picture and the emergence of holes in a semiconductor. Is the "spatial picture" just a useful but incorrect tool for explaining the origin of holes?