hi,
Diffusion is the movement of molecules from the area of greater concentration to the area of lesser concentration. Osmosis on the other hand is the diffusion of water molecules thru the semi-permeable membrane (i.e. cell membrane). It's a special kind of diffusion. Since water is a solvent, it tend to diffuse from lower concentration to the area of greater concentration to balance the concentration of the solution where the cell is subjected.
When a cell is placed in a hypertonic solution, water from the cell will diffuse towards the area of greater concentration ( outside of the cell) making the cell shrink ( the term is Plasmolysis or the shrinking of the cell).
If the cell will be placed in a hypotonic solution, the water outside the cell will move inward; hence, the cell will swell ( this phenomenon is called cytolysis or cell swelling) .
Osmosis happened in plants and animals cells alike. Nevertheless, plasmolysis is fatal to both type of cells while cytolysis is fatal to animals only; since plants have cell wall to push the extra water that would enter the cell (turgor pressure). In illustration, a slice of raddish place in a salt solution wilts, but if place in water becomes firm (turgid). A blood cell placed in water will burst (cytolysis) and will be plasmolyzed when placed in salt solution.
i hope it did help.

julie