cutting tool vs cutter

cutting tool and cutter both are nouns.

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

As nouns, cutting tool and cutter are synonyms defined as:

Other synonyms of cutting tool include cutlery.

cutting tool (noun)	cutter (noun)
a cutting implement; a tool for cutting	a cutting implement; a tool for cutting
	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