Commonly available fish fillets range from 1/3” thick (sole, flounder) to 1.5” thick (salmon, cod). Fish with huge fillets, like tuna and swordfish, are usually sold in steaks (a cross-section cut). Fish with tiny fillets, like sardines and smelts, are sold whole.
Thickness of the steaks does not depend on the type of fish since it’s a cross-section cut. It can be made as thick or thin as the person butchering the fish desires, but traditionally, steaks are around 1” thick.
Whole fish come in all shapes and sizes. They can be as small as anchovies (1/4 inch thick) or as huge as swordfish (almost 2 feet thick). Fish that are over 4" thick or over 8 pounds are rarely cooked whole.
There is a whole spectrum of fish textures from fragile to dense. Here are some examples.
To determine the texture of a fish, bend its fillet or steak and get a feel for its flexibility. If it feels stiff when you bend it and as firm as meat, it is dense. Try that on a piece of swordfish or tuna to get a sense for what a dense fish feels like. If it’s flexible and drapes like fabric, it is fragile. Fillets of fragile fish, like sole or flounder, are so flexible that you can roll them up from head to tail. The other fish textures are somewhere between these two extremes.
Delicate and slightly firm fish lend themselves nicely to any cooking method, so don’t worry if you can’t tell the difference between their textures. The fish at the extremes of the texture spectrum are not as versatile. It's not a good idea to grill fragile fish, such as sole and flounder. They are likely to fall through the grill rack, and there goes your dinner. The dense and firm fish-- like tuna, swordfish, and mahi-mahi don't lend themselves well to poaching and steaming. Their texture resembles that of meat, and they are cooked as such. Can you imagine a poached lamb or pork chop? Neither can I. Firm and dense fish are best cooked with dry, intense heat methods: grilling, broiling, and searing.
Texture is also the deciding factor in whether or not to marinade a fish. Many dense fish tend to dry out during cooking, and can benefit from sitting in an oily marinade for 30 minutes to couple of hours. That’s the secret to juicy swordfish. The only dense fish that can be just as good without a marinade is tuna when cooked very rare. Fish that are not dense do not need a marinade.
Fish fat is the carrier of flavor and all those wonderful omega-3 fatty acids, so it’s nothing to shy away from. The easiest way to evaluate the fat content of a fish is to broil it. If there is a lot of fat left in your broiler dish, it’s a fatty fish. As a general rule of thumb, white fleshed fish are lean, orange and dark fleshed fish are fatty, and cream fleshed fish can be lean, medium, or fatty. The fattier fish have a more succulent moist texture than lean fish and they are easier to cook since they don't tend to dry out.
The flavor of different fish varies from mild to very intense, and it often goes hand in hand with fat content. Most white fleshed fish are mild, cream fleshed fish are moderately flavorful, and dark fleshed fish are intensely flavorful. The fish with orange flesh all belong to the salmon family and they have a very particular, somewhat sweet flavor.
When following fish recipes, it is always possible to use the fish of similar texture, fat content, and flavor intensity. Thickness of the fish rarely makes a difference in substitution. Even the same species can have a huge variation in thickness. But remember that you have to adjust the cooking time, allowing around 8 minutes per inch of thickness. For example, a 1/2 inch thick arctic char fillet cooks twice as fast as a 1 inch thick salmon fillet.