Galactic open and globular clusters (OCs, GCs) appear to inhabit separate regions of the age-mass plane. However, the transition between them is not easily defined because there is some overlap between high-mass, old OCs and low-mass, young GCs. We are exploring the possibility of a clear-cut separation between OCs and GCs using an abundance feature that has been found so far only in GCs: (anti)correlations between light elements. Among the coupled abundance trends, the Na-O anticorrelation is the most widely studied. These anticorrelations are the signature of self-enrichment, i.e., of a formation mechanism that implies multiple generations of stars. Here we concentrate on the old, massive, metal-rich OC NGC 6791. We analyzed archival Keck/HIRES spectra of 15 NGC 6791 main sequence turn-off and evolved stars, concentrating on the derivation of C, N, O, and Na abundances. We also used WIYN/Hydra spectra of 21 evolved stars (one is in common). Given the spectral complexity of the very metal-rich NGC 6791 stars, we employed spectrum synthesis to measure most of the abundances. We confirmed the cluster super-solar metallicity and abundances of Ca and Ni that have been derived in past studies. More importantly, we did not detect any significant star-to-star abundance dispersion in C, N, O and Na. Based on the absence of a clear Na-O anticorrelation, NGC 6791 can still be considered a true OC, hosting a single generation of stars, and not a low-mass GC.