The intermediate disturbance hypothesis (IDH) has been used for several decades as an explanation for the coexistence of species in ecological communities. It is intuitively simple, but deceptively so. We show, via discussion and examples, that the IDH is not one mechanism of coexistence, but rather summarizes a set of similar phenomena that can arise from the action of several different coexistence mechanisms. These underlying mechanisms are defined by the various ways in which species differ in their response to disturbance-induced spatial and temporal variability in resources and environmental conditions. As an example, the original specification of the IDH required patchy disturbances for coexistence. However, because the underlying mechanisms of coexistence can also operate at the within-patch scale, patchy disturbances are not a necessary requirement for coexistence under intermediate-disturbance regimes. These conclusions are illustrated through the analysis of three models: a spatial within-patch model, a spatial between-patch model, and a purely temporal model. All three generate similar patterns of coexistence under intermediate disturbance, yet underlying that coexistence lie at least two quite-distinct mechanisms of species coexistence: the storage effect and relative nonlinearity. The results from our analyses suggest that, as a promoter of species coexistence, the IDH is both broader in scope and richer in detail than has previously been recognized.