Discus are fish from the genus Symphysodon, which currently includes the species S. aequifasciatus, S. discus and S. tarzoo, based on a taxonomic review published in 2006. A review published in 2007 largely came to the same result, but differed in nomenclature.
Koi is an informal name for the colored variants of C. carpio kept for ornamental purposes. There are many varieties of ornamental koi, originating from breeding that began in Niigata, Japan in the early 19th century.