come near vs draw close

come near and draw close both are verbs.

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

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

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

come near (verb)	draw close (verb)
move towards	move or arrange oneself in a comfortable and cozy position
come near in time	pull towards oneself
almost do or experience something	move towards