The aim of this paper is to clarify the conceptual difference which exists between the interactions of composite bosons and the interactions of elementary bosons. A special focus is made on the physical processes which are missed when composite bosons are replaced by elementary bosons. Although what is here said directly applies to excitons, it is also valid for composite bosons in other fields than semiconductor physics. We, in particular, explain how the two elementary scatterings - Coulomb and Pauli - of our many-body theory for composite excitons, can be extended to a, pair of fermions which is not ail Hamiltonian eigenstate - as for example a pair of trapped electrons, of current interest in quantum information.