It's why taxonomy uses latin for this... the definition of english words are based on common usage which isn't going to line up to any kind of scientific categorization. English is always changing and scientific categorization is also always changing when there's more empirical data. These changes are independent of each other so it was wisely decided long ago to not even try to make english words consistent with scientific taxonomy.

So in common usage, yeah it's based around the general shape but it isn't a whale (big mammal) a dolphin (a relatively smaller mammal). A shark might be called a fish but more likely someone will just call it a shark instead of just using just "fish". This is fine for communication among laypeople, if marine biologists are having a conversation about those same animals, they break out the latin and there's no confusion.

Also my understanding is that in medieval times, the word whale actually refereed to a specific species of whale... what we know call the Right Whale, which is nearly extinct. So a word for a species became a word for a group of species and then it was awkward how to refer to that original species. What kind of whale is that? "It's a whale whale... you know the original whale... the proper whale... the right whale." There's actually a paragraph in Moby Dick about this.

English is weird and changes in weird ways. Just use latin if you want to be scientifically precise.