The activation of dinitrogen by coordination to transition metal ions is a widely used and promising approach to the utilization of Earth's most abundant nitrogen source for chemical synthesis. End-on bridging N2 complexes (μ-η1:η1-N2) are key species in nitrogen fixation chemistry, but a lack of consensus on the seemingly simple task of assigning a Lewis structure for such complexes has prevented application of valence electron counting and other tools for understanding and predicting reactivity trends. The Lewis structures of bridging N2 complexes have traditionally been determined by comparing the experimentally observed NN distance to the bond lengths of free N2, diazene, and hydrazine. We introduce an alternative approach here and argue that the Lewis structure should be assigned based on the total π-bond order in the MNNM core (number of π-bonds), which derives from the character (bonding or antibonding) and occupancy of the delocalized π-symmetry molecular orbitals (π-MOs) in MNNM. To illustrate this approach, the complexes cis,cis-[(iPr4PONOP)MCl2]2(μ-N2) (M = W, Re, and Os) are examined in detail. Each complex is shown to have a different number of nitrogen-nitrogen and metal-nitrogen π-bonds, indicated as, respectively: W≡N-N≡W, Re═N═N═Re, and Os-N≡N-Os. It follows that each of these Lewis structures represents a distinct class of complexes (diazanyl, diazenyl, and dinitrogen, respectively), in which the μ-N2 ligand has a different electron donor number (total of 8e-, 6e-, or 4e-, respectively). We show how this classification can greatly aid in understanding and predicting the properties and reactivity patterns of μ-N2 complexes.