Diffusion refers to the movement of a substance from a region of higher concentration to the region of lower concentration. Osmosis refers to the procedure by which the molecules of solvent seems to go through a semipermeable membrane from a region of less concentrated solution to a region of more concentrated solution.
Diffusion takes place in the presence or in the absence of membrane between the two regions of distinct concentration of molecules. On the other hand, osmosis only takes place through a semipermeable membrane, a membrane that inhibits various molecules or particles to freely pass between the two sides of the membrane, while permitting the molecules of water to pass through.