Koi is a kind of Japanese carp, but, etymologically speaking, that's like saying carp is a kind of carp. This is because koi comes from the Japanese word koi, meaning "carp" in general. This was borrowed in 1727, but only as a term for the most common type of Japanese carp- the rest all have different names. Koi in Japanese probably comes from an Old Japanese word with the same meaning and sounding like kopi (there is a citation in the Nihon Shoki, the second oldest book in Japanese). Before that, it's anyone's guess, but it probably derives from a Proto-Japonic root meaning "fish" in general or something of the sort. East Asian languages are always difficult to trace. Fun side note: in Japan, koi can also mean "love" or "affection", so koi have become synonymous with friendships and infatuations in the country. Second side note: because of the increased popularity of koi ponds in landscaping, the word koi is now at its highest usage ever.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.