edge up vs draw close

edge up and draw close both are verbs.

Word	Noun	Adjective	Verb	Adverb
edge up	No	No	Yes	No
draw close	No	No	Yes	No

As verbs, draw close is a hypernym of edge up; that is, draw close is a word with a broader meaning than edge up:

Other hypernyms of edge up include approach, come near, come on, draw near, go up, near.

edge up (verb)	draw close (verb)
push one's way into (a space)	move or arrange oneself in a comfortable and cozy position
	pull towards oneself
	move towards