man-eater vs mackerel shark

man-eater and mackerel shark both are nouns.

Word	Noun	Adjective	Verb	Adverb
man-eater	Yes	No	No	No
mackerel shark	Yes	No	No	No

As nouns, mackerel shark is a hypernym of man-eater; that is, mackerel shark is a word with a broader meaning than man-eater:

man-eater: large aggressive shark widespread in warm seas; known to attack humans
mackerel shark: fierce pelagic and oceanic sharks

man-eater (noun)	mackerel shark (noun)
large aggressive shark widespread in warm seas; known to attack humans	fierce pelagic and oceanic sharks
a person who eats human flesh