The results from two approaches, those from the coupled cluster expansion (CCA), and those from the Green's function formalism (GFF), are compared in perturbation theory. The atoms discussed consist of a nondegenerate core, plus or minus two electrons (two particle (2P) and two hole (2H) systems), such that the resulting atoms also have non-degenerate ground states. The specific cases considered are the He++ -He pair through third order, and, very briefly, the Be++ -Be pair in second order. The corresponding 2-electron non-relativistic (NR) Bethe-Salpeter (BS) Green's functions are 0-, 2-, or 4-electron (rather than just 0-electron, i.e., vacuum) expectation values. The general equivalence of the various approaches is demonstrated in detail for He: On the one hand, the 2P and 2H versions of the CCA are shown to give the same result for the ground state energy in these orders, provided the same atom is described in both versions. On the other hand, the CCA and the GFF are shown to yield equal results.