You can have an aquarium with something other than fish in it (frogs, turtles, shellfish, etc.) However, the majority of aquarium posts will be about fish, and all fish posts will be about aquariums.
The consequence of this is that likely the vast majority of fish questions will have both tags. However, there will be some questions with the aquarium tag paired with another animal tag (such as frogs or turtles), and there could even be questions with only the aquarium tag and no animal tag (for example, a question about aquarium maintenance or repair).
Most people I know here in semi-temperate Oregon have had pond fish, which are often as much pets as the aquarium fish. I would think that aquarium or pond tags would be related to the environment and fish or frogs or turtles the animals involved.
Examples: "What is the best way to keep my aquarium at a constant temperature?" - tag aquarium, don't tag fish "My aquarium ranges in temperature from X degree to Y degree over the course of a day is that safe for my BREED Z fish?" - tag aquarium and fish "How do I train my fish to swim through a hoop?" - tag fish and not aquarium, pond, ... "What is the best pond liner to use?" - tag pond and not fish "Is pond liner brand X safe for turtles?" - tag pond and turtle
Because the vast majority of aquarium posts will be about fish, it seems like a lot of work to require that all of these questions be tagged with two tags. The tag aquarium could be used for these fish posts, and fish could be made a synonym for aquarium. For questions on frogs or turtles that are kept in aquariums, those questions could be tagged both with aquarium as well as the animal tag (i.e. frogs.