Not at all.
If I place AgCl, as an example, in water, shake and stir until equilibrium is attained, I will have aome AgCl in solution as Ag^+ and Cl^-, I will have some AgCl (undissociated) dissolved in the solvent, water, and I will have some solid AgCl that will settle to the bottom of the beaker. That will be a saturated solution.
A slightly different example: sugar and water.
If I place a spoonful of table sugar in water (let's say 250 mL), and shake and stir until all of it is dissolved, I will have a solution of sugar in water. Placing more sugar in the water, if it dissolves completely, makes a more concentrated SOLUTION of sugar. If I keep adding sugar, and it keeps dissolving, I simply prepare a more and more concentrated solution. At some point, however, the water holds as much sugar as it can and no more sugar will dissolve, no matter how long I stir or how long I shake. At that point, we have a saturated solution. To KNOW we have a saturated solution, we must SEE some undissolved sugar at the bottom of the beaker. There will be an equilibrium between the sugar molecule in solution and the sugar molecules at the bottom of the beaker. This is not a static equilibrium but a dynamic one in which a few sugar molecules are dissolving and an equal number of dissolved molecules are recrystallizing at the bottom of the beaker. The net, however, is that no matter how much more sugar we add, no more will go into solution. The additional sugar will add to that already collected at the bottom of the beaker. I hope I've not taken your question our of context since there were four or five possible scenarios from the answers. Please follow up if needed.