draw close vs draw near

draw close and draw near both are verbs.

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

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

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

draw close (verb)	draw near (verb)
move or arrange oneself in a comfortable and cozy position	move towards
pull towards oneself
move towards