Examples of supersaturated solutions appear in the link. Saturated solutions contain the same amount of solute that would be in equilibrium with undissolved solute. Any mixture from which a solute has precipitated gives a saturated solution with respect to that solute. Why, because there is equilibrium between undissolved solute and dissolved solute.
An unsaturated solution is a solution that contains less than an equilibrium quantity of solute. Sugar in tea is an unsaturated solution.