When the Bose-Einstein and the Fermi-Dirac statistics were first formulated and explored, their conceptual foundations raised more questions than the formal apparatus of the theories could answer. The interpretive flexibility of the theories, however, did not deter physicists from probing their applicability to various physical systems and integrating them into networks of practice. It was only in the following two decades, through the tumultuous developments of the 1930s and early 1940s, that a unified interpretation was formulated, which viewed both quantum statistics as consequences of a radical break from the classical conception of radiation and matter. After a brief survey of the interpretative diversity of the early period (1924-1926), some reformulations and uses of the quantum statistics in the 1927-1946 period, for example by George Uhlenbeck, Ralph Fowler, Fritz London, Erwin Schrödinger, and Paul Dirac, are examined, with a focus on the role played by local contexts and traditions of theoretical practice in the eventual emergence of the new foundational categories of “bosons” and “fermions”.