All aquarium fish belong to the Eukaryote Domain, Animalia Kingdom, Chordata Phylum, Vertebrata Subphylum, Osteichthyes Superclass (bony fish), and Actinopterygii Class (ray-finned fish). From there, this aquarium fish chart breaks it down further:
OSTARIOPHYSI SUPERORDER:
Cypriniformes Order (Carps)
Cyprinid Family
BARBS Europe, Asia e.g. - Tiger Barb (Puntius tetrazona)
DANIOS Asia e.g. - Zebra Danio (Danio rerio)
RASBORAS Asia e.g. - Harlequin Rasbora (Trigonostigma heteromorpha)
MINNOWS Asia e.g. - White Cloud Mountain Minnow (Tanichthys albonubes)
'SHARKS' Asia e.g. - Bala Shark (Balantiocheilos melanopterus)
GOLDFISH Asia e.g. - Goldfish (Carassius auratus)
Cobitid Family
LOACHES Europe, Asia, Africa e.g. - Kuhli Loach (left) & Clown Loach (right) (Pangio kuhlii & Chromobotia macracanthus)
Characiformes Order (Tetras & Relatives)
Characid Family
TETRAS Americas, Africa e.g. - Neon Tetra (Paracheirodon innesi)
PACUS Americas e.g. - Black Pacu (Colossoma macropomum)
Gasteropelecid Family
HATCHETFISH Americas e.g. - Common Hatchetfish (Gasteropelecus sternicla)
Lebiasinid Family
PENCIL FISH Americas e.g. - Three-lined Pencil Fish (Nannostomus trifasciatus)