Why do Ca-Ca distances get shorter in ionic structures, as compared to the metal?
Simply put, the distance is measure from the center of the atoms. In the metal, the uncharged Ca atoms are kept at the van der waals contact distance.

In the ionic compounds the atomic radii of the Ca2+ ions have shrunk due to the loss of the outer shell electrons. Furthermore, negative ions cancel out the repelling charges and allow the Ca2+ ions to pack even closer together.