The "Ancient Codfish" is from Bagpuss [very enjoyable but episode 6 wouldn't be aired today].
Codfish is just a fancy name for Cod. There are 3 usually recognised species of them [Atlantic, Pacific and Greenland] and they're related to Haddock and Pollock.
In their genus, there is actually a fourth fish, the other being the Alaska Pollock, Snow Cod or Bigeye Cod. It is a cod but it isn't recognised as such by most :[









