Connection between zeta and cutoff regularizations of Casimir energies

We study the connection between zeta- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to minimal finite parts which do not coincide. We determine the relationships among the various coefficients appearing in one approach and the other. We discuss the agreement with our predictions in the case oi scalar fields in d-dimensional boxes under periodic boundary conditions. Finally, we apply our results to massless scalar fields in balls, an example where ambiguities remain under the physical prescriptions usually imposed to extract a finite result.