Melville himself served on a whaler and AFAIK the descriptions of actual whaling and processing of whales at sea are basically accurate with some embellishment. Open to being wrong about that though as I am by no means an 1800s whaling expert.
It's been a long time, I read it right after reading the Eric Dolin book about american whaling and coming out of that some of the details about nantucket and its fleet & practices at that time were off but I'm not going to be able to come up with citations on anything.
He also messes with some of the shipboard social dynamics for the sake of the story, uses names for some of the positions that were not used in the american whaling fleet, shifts responsibility for certain things around so they'll land on named characters, standard literary moves like that.
It's probable that all of these were intentional to serve the story. And I'm not an expert either which makes simple embellishment hard to spot. I'm mostly just pointing out that asserting what anyone "knows" about whales from reading moby dick is tricky.
You're also of the opinion that whales are fish?
Different category but well explained here https://eukaryotewritesblog.com/2021/05/02/theres-no-such-th...
Whales need to take breaths on the surface, unlike fish, which can stay underwater basically indefinitely. Without that difference, whaling would be a lot more complicated, if not outright impossible, especially in the 19th century - you just can't catch a huge solitary animal in an ocean on purpose if it doesn't have to surface from time to time. Or only with sheer luck.
Even the ancient whalers were aware of the fact that whales need to breathe, and thus, at the very least, could say "well, these are some rather special fish, you know".