We present an overlooked but important property of modern coexistence theory (MCT), along with two key new results and their consequences. The overlooked property is that stabilizing mechanisms (increasing species' niche differences) and equalizing mechanisms (reducing species' fitness differences) have two distinct sets of meanings within MCT: one in a 2-species, and another in a general multispecies context. We demonstrate that the 2-species framework is not a special case of the multispecies one, and therefore these two parallel frameworks must be studied independently. Our first result is that, using the 2-species framework and mechanistic consumer-resource models, stabilizing and equalizing mechanisms exhibit complex interdependence, such that changing one will simultaneously change the other. Furthermore, the nature and direction of this simultaneous change depend sensitively on model parameters. The second result states that while MCT is often seen as bridging niche and neutral modes of coexistence by building a niche-neutrality continuum, the interdependence between stabilizing and equalizing mechanisms acts to break this continuum under almost any biologically relevant circumstance. We conclude that the complex entanglement of stabilizing and equalizing terms makes their impact on coexistence difficult to understand, but by seeing them as aggregated effects (rather than underlying causes) of coexistence, we may increase our understanding of ecological dynamics.