A simple algebraic model is used to show that Hirshfeld surfaces in condensed phases may be understood as approximations to the interatomic surfaces of the theory of atoms in molecules. The conditions under which this similarity is valid are explored, and both kinds of surfaces are calculated in the LiF and CS2 crystals to illustrate the main results. The link between Hirshfeld and interatomic surfaces provides a physical ground to understand the usage of the former to visualize intermolecular interactions.