In this paper, the contribution of many-body effects to the X-ray photoelectron spectroscopy, XPS, of an NO molecule is studied using wavefunction theory where the specific consequences of different many-body terms are examined and contrasted. It is shown that there is a differential importance of the many-body effects for the different configurations involved in the XPS. These are the ground, initial state configuration and final, N(1s) and O(1s) core hole ionic configurations. The consequences of the many-body effects are examined for the binding energies, BEs, to the two final state multiplets, triplet, and singlet, for each of the core ions and for the relative intensities of the XPS transitions to these multiplets. The many-body effects examined are those described as static effects that arise for individual terms that are important. The objective is to understand the chemical and physical origins that determine the importance of the correlation effects for the XPS, rather than to obtain very accurate predictions of the BEs. An important theoretical construct that is tested and justified is the equivalent core approximation where the core-ionized atom is replaced by the next higher element in the periodic table. This construct allows us to establish a correlation for the relative importance of the many-body effects in terms of effective charges of the different atoms. This is a correlation that has not been considered before and that we expect may have general relevance. The potential of the effects that we have identified for the XPS of NO to be relevant for the XPS of more complex, condensed phase systems is considered.