This question already has an answer here:
What's the halachik classification as to why Dolphins aren't kosher?
Is it because:
Dolphins are like a fish
they live in the ocean and thus the Torah considers them a fish and they don't have fins and scales?
Dolphins are like other mammals
they're a mammal and like the other kosher mammals they don't have split hooves and chew their cud?
Practical difference: (H/T Heshy)
What warning would witnesses have to give to someone who's about to eat Dolphin;
"don't eat that non-kosher fish!" or "don't eat that non-kosher animal!"