A dace is a small fish that can be one of many different species. The unmodified name is usually a reference to the common dace (Leuciscus leuciscus). This, like most fishes called "daces", belongs to the family Cyprinidae, mostly in subfamily Leuciscinae.
Daces in the Cyprinidae:
Common dace, Leuciscus leuciscus
Chinese mud carp, Cirrhinus chinensis (called "dace" in Hong Kong) or mud carp (Cirrhinus molitorella)
Columbia River dace, Ptychocheilus oregonensis (a pikeminnow)
Desert dace, Eremichthys acros (a monotypic genus)
European daces, genus Leuciscus
Fallfish, Semotilus corporalis (a creek chub called "dace" in Canada)
Horned dace, Semotilus atromaculatus (a creek chub)
Japanese dace Tribolodon hakonensis, genus Tribolodon
Korean splendid dace, Coreoleuciscus splendidus (a monotypic genus)
Lake Candidus dace, Candidia barbatus (a monotypic genus)
Mexican daces, genus Evarra
Moapa dace, Moapa coriacea (a monotypic genus)
Northwest dace, Mylocheilus caurinus (a peamouth)
Pearl dace, Margariscus margarita (a monotypic genus)
Ponto-Caspian daces, genus Petroleuciscus
Redbelly daces, genus Phoxinus
Redside daces, genus Clinostomus, e.g.
Redside dace Clinostomus elongatus
Rosyside dace Clinostomus funduloides
Relict dace, Relictus solitarius (a monotypic genus)
Riffle daces, genus Rhinichthys (including Tiaroga)
Saskatchewan dace, Platygobio gracilis (a flathead chub)
Shining dace, Semotilus corporalis (a creek chub)
Spikedace, Meda fulgida (a monotypic genus)
Spinedaces, genus Lepidomeda
Daces not in Cyprinidae
Sea dace, the European seabass (Dicentrarchus labrax) of the Moronidae
