Diffusion is the net movement of molecules from a region of high concentration to a region of lower concentration.
Osmosis is the net movement of water through a partially permeable membrane, from a solution of less negative water potential, to a solution of more negative water potential.
Both Diffusion and osmosis occur down the concentration gradient.
Basically they are the same thing, but osmosis is the diffusion of water in solution, rather then gaseous diffusion. We use the term osmosis to differentiate between gaseous transport and water movement.
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