Koi
The major named varieties include:Goldfish (金魚) were developed in China more than a thousand years ago by selectively breeding Prussian carp for color mutations. By the Song dynasty (960–1279), yellow, orange, white, and red-and-white colorations had been developed. Goldfish ("Carassius auratus") and Prussian carp ("Carassius gibelio") are now considered different species. Goldfish were introduced to Japan in the 16th century and to Europe in the 17th century. Koi, though, were developed from common carp in Japan in the 1820s. Koi are domesticated common carp ("Cyprinus carpio") that are selected or culled for color; they are not a different species, but a subspecies, and will revert to the original coloration within a few generations if allowed to breed freely.
Wakin goldfish
The wakin has many popular cultures and beliefs in the history of Japanese goldfish. The wakin goldfish, in Japanese terms, are any 'Huna' bodied goldfish with a single tail (in reference to the popular common goldfish), double tail, or triple tail, while in US, a wakin is simply a double tail goldfish with a long body. Wakins are also popularly seen in red and white, that are prized for competition. Other colors of wakins have made from it, such as chocolate, blue, red, white, orange, and yellow. There is also a calico wakin, but for some reason, the regards to its color process, the calico wakin is not a full-blooded wakin line.