cutter vs edge tool

cutter and edge tool both are nouns.

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

As nouns, edge tool is a hyponym of cutter; that is, edge tool is a word with a more specific, narrower meaning than cutter:

cutter: a cutting implement; a tool for cutting
edge tool: any cutting tool with a sharp cutting edge (as a chisel or knife or plane or gouge)

Other hyponyms of cutter include bolt cutter, cigar cutter, die, glass cutter, tile cutter.

cutter (noun)	edge tool (noun)
a cutting implement; a tool for cutting	any cutting tool with a sharp cutting edge (as a chisel or knife or plane or gouge)
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