white shark vs man-eater

white shark and man-eater both are nouns.

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

As nouns, white shark and man-eater are synonyms defined as:

white shark and man-eater: large aggressive shark widespread in warm seas; known to attack humans

Other synonyms of white shark include Carcharodon carcharias, great white shark, man-eating shark.

white shark (noun)	man-eater (noun)
large aggressive shark widespread in warm seas; known to attack humans	large aggressive shark widespread in warm seas; known to attack humans
	a person who eats human flesh