The Tora says: “These you may eat, of all that are in the waters. Everything in the waters that has fins and scales … you may eat. But anything in the seas or the rivers that has not fins and scales … is forbidden to you” (Lev. 11:9-11). Both elements, scales (qasqeset) and fins (senapir) are necessary for a fish to be considered Kosher. The Rabbis of the Talmud taught that although both elements are necessary, all fish with scales also have fins. Thus, in practical terms, a Kosher fish is identified simply by the presence of scales (the scales are obviously removed in the process of cleaning the fish). Illustrations: Salmon, Tuna, White fish, etc. are Kosher (more specifically tabor) because they have scales. Crustaceans such as lobster or squid, clams, oysters, etc. are not Kosher (they are ta-me) because they lack scales.
SCALES: Some “scales” not considered Kosher by Jewish Law. For example, when the scales are part of the fish-skin and cannot be removed without damaging the skin. Illustrations: Sturgeon, although it has primitive bony-plates on its sides, is not Kosher because its scales (Gandoid scales) cannot be removed without damaging the flesh. Sharks are also non-Kosher fish. Their skin is covered with tiny teeth-like armor (placoid scales) which look like scales.
NAMES: When looking for a Kosher fish bear in mind that the names might vary from place to place. A given specie of fish might be known by five or more names and some of those names might sound Kosher. Illustration: We know that salmon is Kosher. But what about “Rock Salmon”? Is Rock salmon a standard variety of salmon, like Pink Salmon, Atlantic Salmon, Wild Salmon? Rock Salmon (very popular in England) is a non-Kosher fish, a small shark known as spiny-dogfish, which bears no relationship to the common Kosher specie of true salmon.
For a comprehensive list of Kosher and non-Kosher fish see this