Good question. It matters on what definition you use. For me, a domestic animal is one that is bred in captivity, with marked differences from the wild phenotype, for the purpose of food, work or as a pet. That means that a wild caught fish is not domesticated. However, there is also a length of time/number of generations from wild that comes into play and that is subjective. A f1 cichlid is not domesticated.
In my work, I've only heard of goldfish and koi being called domestic fish. An argument could be made however, to include other aquarium fish - angelfish, etc. that have been in captivity for 200 years or so. Would clownfish be considered domesticated after only 50 years in culture? I would say not because many breeders augment with wild stock along the way. There are legal definitions for "domestic animal" the USDA uses, but it can also mean any animal originated from the US.
Jay