knife edge vs cutting edge

knife edge and cutting edge both are nouns.

Word	Noun	Adjective	Verb	Adverb
knife edge	Yes	No	No	No
cutting edge	Yes	No	No	No

As nouns, knife edge and cutting edge are synonyms defined as:

knife edge and cutting edge: the sharp cutting side of the blade of a knife

knife edge (noun)	cutting edge (noun)
the sharp cutting side of the blade of a knife	the sharp cutting side of the blade of a knife
	the position of greatest importance or advancement; the leading position in any movement or field