Near-edge and extended x-ray-absorption fine-structure measurements from a wide variety of oxidized Si nanocrystals and H-passivated porous Si samples, combined with electron microscopy, ir absorption, forward recoil scattering, and luminescence emission data, provide a consistent structural picture of the species responsible for the luminescence observed in these systems. For porous Si samples whose luminescence wavelengths peak in the visible region, i.e., at {lt}700 nm, their mass-weighted-average structures are determined here to be particles (not wires) whose short-range character is crystalline and whose dimensions---typically {lt}15 A---are significantly smaller than previously reported or proposed. Results are also presented which demonstrate that the observed visible luminescence is not related to either a photo-oxidized Si species in porous Si or an interfacial suboxide species in the Si nanocrystals. The structural and compositional findings reported here depend only on sample luminescence behavior, not on how the luminescent particles are produced, and thus have general implications in assigning quantum confinement as the mechanism responsible for the visible luminescence observed in both nanocrystalline and porous silicon.