Where the two electrons are paired in the same orbital these two terms cancel so we are left to just sum the electron density of the unpaired electrons. This gives the spin density. It is called the free valence and is related to an old idea that radicals will attack centres with free or available valence. The unfree valence is taken as the sum of the bond orders for the bonds involving a specified atom. The question then is how much is free.
Charge densities give a measure of the charge on an atom.
If it is less than one, the atom is positively charged. These can be used in some cases as predictors of the most likely site for electrophilic and nucleophilic substitution. However, as you will discover elsewhere in these pages, in some cases all charge densities in some hydrocarbons are one, so charge density does not act as a discriminator in predicting substitution. Bond orders can be related to bond lengths, as we will cover in an exercise in these materials. Spin densities have proved particularly useful.