Hi Anders,
Do you want to recognize an individual fish or a type of fish (salmon vs shark?)??
in any of the cases, you’d need many many images of fish to train the model.
On the faces feature you mentioned, what I think they are doing is, they know how to find a face on a picture. That’s kind of easy as faces are usually all similar (eyes, nose, mouth). After that, you can calculate an embedding and use something like nearest neighbors to find similar faces and create groups of faces that are from the same person.
This same algorithm can be used for a lot of things, not only faces.
I hope it helped