You missed the Buffalo and Siamese Carp and the Giant Barb which is the worlds largest Cypranid and grows to over 3m in length and weighs in at over 300kg (Mekon river system in China)
The only Carp in your list above in our SA waters are the Grass Carp, and the Cyprinidae, ie the Carpio (Mirror, Common, Koi) The leather, Common and Mirror carp are the same fish and interbreed with the common carp gene strain being dominant. The scale patterns are the only variation in the anatomy of the fish.
The Bighead Asian Carp is not found in South Africa, there is however a viable population of Hypophthalmichthys molitrix (silver carp), the Chinese Silver Carp in the Olifants river from below the Loskop dam wall all the way to the indian ocean.
Tinca-Tinca or the Tench is found in the Breede river and some private resevoirs in the Western Cape.
The Mudfish is of the Labeo species and we have the Orange River, Purple, Red Nose, Red-Scaled and Leaden mudfish, Clanwilliam Sawfin, Tugela Mudfish in our river systems. These are also a sub species of Cyprinadae and are known as a whole in the larger group as African Carp,
American Buffalo Carp