What’s the difference between oxidative phosphorylation and chemiosmosis, what’s the purpose of the two?

In all cells, these are both part of the ATP production process (in eukaryotic cells it takes place in the mitochondria, in prokaryotic cells in the cytosol and inner membrane). Oxidative phosphorylation is a series of redox reactions that release energy used to synthesize adenosine triphosphate (ATP). A number of intermembrane enzymes — the electron transport chain (ETC) — together build up a proton gradient, the energy of which is used to drive the enzyme F𝑂F1 ATPase, which phosphorylates ADP and inorganic phosphate (P𝑖), forming ATP. Chemiosmosis is when H+ ions passively move “downstream” across a semipermeable membrane (from a higher to a lower ion concentration). The proton flow across the mitochondrion inner membrane, down the H+ gradient built up by the ETC (as described above) is a prime example of chemiosmosis.