There are many different species of fish. Too many to list here on this site and too many to name aloud. But I will provide a list of a short few breeds of fish.
Sand Bass
Perch
Tilapia
Catfish
Koi Fish (non-edible; or rather wrong to eat...kept as pets in Japanese and Chinese culture)
Puffer Fish (semi non-edible; Japanese breed is toxic to the point of death if prepared incorrectly)