Osmotic equilibrium is the term used to indicate that the concentration of a solute in water is the same on both sides of a semi-permeable membrane. While the water still passes through the membrane, there is no gain or loss on either side.
Osmosis is the process by which water moves through a membrane that does not allow particles larger than the water molecules to pass due to the different concentrations of solute on either side of the membrane. It is diffusion caused by osmotic pressure. The water moves from the side that has a lower solute concentration to the side that has a higher solute concentration. This is done regardless of the amount of water on either side and can result in one side of the membrane having larger volume of water.
When the solutions on both sides of the membrane have achieved osmotic equilibrium they are isotonic solutions. Until they are in equilibrium, the solution with the higher concentration of solute is called hypertonic and the one with the lower concentration of solute is called hypotonic. The fundamental process of osmosis is the reason different solutions cause dehydration and why eating salty foods causes thirst. The high concentration of salt molecules draws water out of the cells of the body.