Okay, so we need to know that these two phenomena are implied in cell homeostasis (the regulation of their internal concentration of nutrients).
* Whit internal concentrations of nutrients I refer to the variable amount of salts, for example, but also water, and waste materials.
Well, so in general terms, diffusion is the movement of those nutrients (solutes specifically) from highest to lowest concentrations. While osmosis is the movement of water, specifically, from lowest to highest concentrations.
There's something important we have to consider to aboard the osmosis concept, and it's that the concentration or amount of solvent (usually water) depends on the concentration of the solutes (that could be other nutrients, like salts or minerals). And these differences in water amount and solute concentrations we place them between out of the cell, and within the cell (separated media by the cell membrane).
We can also differentiate diffusion and osmosis in other words by the fact that the former usually occurs in favor of the concentration gradient (passive diffusion, which doesn't need the use of ATP and; in active diffusion these solutes are moved by the use of ATP by the cell. Solutes can be liquid, solid, and gas particles), while the latter occurs against that gradient only for liquid solvents (like water).