Supported CuOx nanoparticle catalysts contain Cu cations in different chemical states and local coordination spheres. These Cu cations, together with vicinal lattice oxygen atoms, form Cu cation-O anion pairs that are effective for oxidation catalysis. Notably, CuOx nanoparticles catalyze the C-H bond activation of methanol, including the oxidative dehydrogenation as well as direct dehydrogenation catalytic cycles, depending on the availability of O2 as the co-oxidant and the number of the reactive oxygen atoms within the CuOx particles. Herein, we investigate the structural dynamics of the CuOx nanoparticles anchored on a variety of supports of non-reducible SiO2, activated carbon, as well as reducible TiO2 support, leading to Cu particles of different average diameters and, for those deposited on TiO2 support, the formation of interfacial Cu-O-Ti moieties. The different Cu species acquire their respective catalytic roles in methanol and CO oxidation reactions, leading to contrasting reactivity trends in response to the presence of water vapor. For methanol activation, Cu-O moieties catalyze the C-H scission of methanol in Mars-van Krevelen chemistry, initiated with an initial O-H bond scission, before the sequential kinetically relevant C-H bond scission. The depletion of the lattice oxygen atoms leads to the reduction of Cu(II) to Cu(0), and to the transition of mechanism from the C-H scission on Cu-O to that on Cu-Cu site pairs. On CuOx particles, Cu-O-Cu sites, prevalent on large Cu particles are most effective for the C-H bond scission of methanol. These sites, however, are much less effective for CO oxidation than the Cu-O-Ti interfacial moieties, created by depositing the CuOx on TiO2 surfaces. A detailed kinetic analysis led us to conclude that these Cu sites, with their different local environments and oxidation states, acquire different catalytic roles in oxidation reactions.