man-eater vs man-eating shark

man-eater and man-eating shark both are nouns.

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

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

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

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

man-eater (noun)	man-eating shark (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