I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that the Boltzmannian framework of statistical mechanics assumes and relies on (...) the ontology-first approach, whereas the Gibbsian framework should assume the theory-first approach. -/- . (shrink)