I will take defects in solids as an example (although other examples are applicable). The formation energy applies to isolated non-composite (for example isolated vacancy) defects as well as to defect clusters or (complex or composite , name it as you wish, but as an example the complex formed between three vacancies ). This formation energy expresses the energy penalty that has to be paid in order to form the defect. Thus, it is the quantity that determines the concentration of a particular defect.
The binding energy is applicable to defect complexes. It is a measure for the thermodynamic stability of the complex against dissociation into its constituents. The complex whose binding energy is such that it is not stable thermodynamically (-ve or +ve depending on the sign convention you wish) should not form under equilibrium conditions.