Osmosis is a particular type of diffusion in which water crosses a semi-permeable membrane to an area with a greater solute concentration, whereas standard diffusion often allows the free movement of both solutes and solvent toward equilibrium. Diffusion in general is the net movement of molecules in solution from areas of higher concentration to areas of lower concentration. Osmotic pressure is potentially very powerful, with osmotic pressure being the only force necessary to move water from the roots to the tops of the tallest trees in the world.
When water dissolves another substance, it is because the polar water molecules and the solute attract one another. Each atom, ion or molecule of solute has a charge in at least one region that attracts one side or another of the water molecule. As such, as many water molecules as possible tend to gather around each particle of solvent. In liquid water, all molecules are in constant, random motion around each other. However, because of the attraction, the water molecules are slightly more likely to move toward particles of solute than they are away from them, and solute particles are more likely to move toward water molecules than other particles of solvent. This net movement results, gradually, in an even distribution of the solute. In osmosis, only the water molecules can move to equalize concentrations.