In short
Diffusion is the movement of particles from a region of higher concentration to a region of lower concentration. Osmosis is the diffusion of water through a partially permeable membrane.
Neither needs energy from the cell. In osmosis, water moves from the more dilute solution (higher water potential) to the more concentrated one (lower water potential). A plant cell in pure water takes in water and becomes firm, or turgid. In a strong salt solution it loses water and shrinks away from the wall, which is plasmolysis.
A potato strip left in strong salt solution becomes limp and shorter, because water leaves its cells by osmosis. In pure water the strip becomes firm and longer.
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