border on vs approximate

border on is not an adjective while approximate is an adjective.

Word	Noun	Adjective	Verb	Adverb
border on	No	No	Yes	No
approximate	No	Yes	Yes	No

As verbs, approximate is a hypernym of border on; that is, approximate is a word with a broader meaning than border on:

border on: come near or verge on, resemble, come nearer in quality, or character
approximate: be close or similar

Other hypernyms of border on include come close.

border on (verb)	approximate (verb)
come near or verge on, resemble, come nearer in quality, or character	judge tentatively or form an estimate of (quantities or time)
	be close or similar