cutter vs cutting tool

cutter and cutting tool both are nouns.

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

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

Other synonyms of cutter include cutlery.

cutter (noun)	cutting tool (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