There are 12 shallow water fish used in quests
There are 12 Dungeon fish used in quests
There are 18 Deep Water fish used in quests
There are 12 crustaceans (6 named lobsters, 6 named crabs) used in quests
The rule of thumb is that if a fish type weighs something other than 10 stone, and doesn't stack with others of its type, it isn't used in a quest (it will also be some odd color). Note that fish that look like the old pre-HS fish can be bugged temporarily to weigh 1 stone each when pulled from stacks, but revert if you cross a server line with them.
crustaceans do stack, but the ones used in quests all weigh 5 stone each. If the crustacean weighs other than 5 stone, or is an odd color/doesn't stack, it is not a quest type.
Note that the Mud Puppy & Red Herring are SA quest fish that are really just variations on the old "Big Fish", and I think their quests are limited to 1 per character each.