edge tool vs cutting tool

edge tool and cutting tool both are nouns.

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

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

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

Other hypernyms of edge tool include cutlery, cutter.

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