cutter vs cutting implement

cutter and cutting implement both are nouns.

Word	Noun	Adjective	Verb	Adverb
cutter	Yes	No	No	No
cutting implement	Yes	No	No	No

As nouns, cutting implement is a hypernym of cutter; that is, cutting implement is a word with a broader meaning than cutter:

cutter (noun)	cutting implement (noun)
a cutting implement; a tool for cutting	a tool used for cutting or slicing
a boat for communication between ship and shore
a sailing vessel with a single mast set further back than the mast of a sloop
someone whose work is cutting (as e.g. cutting cloth for garments)
someone who carves the meat
someone who cuts or carves stone