I've finally found an answer. I had to take a closer look at and contemplate it. And bazinga, that's the answer. To see, sehen, is hardly more than visual perception. 'sich etwas ansehen' is to look at or to watch something. And the next stage is to observe something, etwas betrachten. Siehst du den Fisch? Schau ihn dir an - Do you see the fish? Take a look at it. Anschauen and ansehen are mostly interchangable. Most important: The example says 'ansehen', which needs 'sich' contrary to 'sehen'. Without sich, it might work, too, but has a different meaning, as far as I'm aware and is then interchangable with betrachten: regard or consider x as y.
I find the cat particularly fitting, since any given translation can be applied: The cat sees the fish. It's watching the fish, examining the fish's scales, since the cat considers the fish a delicious dinner. – Die Katze sieht den Fisch. Sie sieht ihn an, betrachted die Schuppen des Fisches genau, da sie ihn als leckeres Abendessen ansieht.
Yes, exactly. Sich etwas ansehen/anschauen = to watch orlook at something. Etwas ansehen = regard or consider something as something.