How does ionic radius differ from atomic radius?

The removal of the valence electron(s) from a metal atom leaves us with an ion that has one fewer shell of electrons, and a (much) smaller particle.

The addition of another electron to a chlorine atom increases the repulsion among all electrons, causing the chloride ion to be slightly larger than the chlorine atom. This increase in size is generally true of nonmetallic atoms that become negative ions.

Also, it should be said that when scientists attempt to measure the radius of an atom or ion, what they actually obtain is the distance between adjacent nuclei in a crystal of the element being treated.

This must be done, because there is no true boundary to an atom as there is no boundary to any orbital. Thus, it cannot be said that the valence shell of an atom (or ion) ends at any particular distance from the nucleus.

Therefore, the measurement we get for the distance between nuclei depends on the particular substance in which we find the particles.

If I measure the distance between two chlorine atoms in a molecule of chlorine gas, I will get a certain value. If instead, I measure the distance between a sodium ion and a chloride ion in a crystal of NaCl, I will get a quite different value for the radius of the chloride ion (even if I take into account the fact that the bond length involves a smaller sodium ion).