The only differences between a fish stew and a fish soup are the proportion of liquid to solids and the fact that some soups are pureed, which makes the cooking time almost irrelevant. Stews are trickier to make because the cooking liquid has to have the correct consistency and flavor at the same time the fish is perfectly cooked.
For fish stews of a more rustic character, whole fish are thrown into a pot of water—often seawater—or water combined with a little shallot or onion and sometimes red or white wine, and then the liquid is boiled until the fish are done. The result isn’t bad if the fish are fresh. But such a concoction also requires dissecting the fish at the table and often leaves the cooking liquid without much flavor or with the flavor of raw wine. A solution to both these problems is to fillet the fish (or buy it filleted and ask for the head and bones), make the cooking liquid ahead of time, and then cook the fillets in the cooking liquid at the last minute. If you make a fish stew with fillets that have different thicknesses, you may need to add them at different times or bake them in the oven as described below.