come on vs draw close

come on and draw close both are verbs.

Word	Noun	Adjective	Verb	Adverb
come on	No	No	Yes	No
draw close	No	No	Yes	No

As verbs, come on and draw close are synonyms defined as:

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

come on (verb)	draw close (verb)
occur or become available	move or arrange oneself in a comfortable and cozy position
appear or become visible; make a showing	pull towards oneself
develop in a positive way	move towards
start running, functioning, or operating
move towards