ax vs edge tool

ax and edge tool both are nouns.

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

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

ax: an edge tool with a heavy bladed head mounted across a handle
edge tool: any cutting tool with a sharp cutting edge (as a chisel or knife or plane or gouge)

ax (noun)	edge tool (noun)
an edge tool with a heavy bladed head mounted across a handle	any cutting tool with a sharp cutting edge (as a chisel or knife or plane or gouge)

ax (verb)	edge tool (verb)
terminate
chop or split with an ax