All Koi belong to one species, CYPRINUS carpio. There are numerous colour varieties which are the result of cross-breeding (i.e. breeding closely related types together) with the outcome being that of more stable varieties.
Learning to recognize the different varieties is made simpler when you have an understanding of the various classifications in which they are grouped. Some types are classified under one group, such as the popular KOHAKU, whilst others are a compilation of several types, for example HIKARIMONO (single coloured, metallic koi).
Of couse, every Koi is unique, although prize-winning Koi are set to certain standards, pattern diversity is acceptable in most varieties.
(Canadian Koi & Pond)