approaching vs closing

approaching and closing both are nouns.

Word	Noun	Adjective	Verb	Adverb
approaching	Yes	Yes	No	No
closing	Yes	Yes	No	No

As nouns, closing is a hyponym of approaching; that is, closing is a word with a more specific, narrower meaning than approaching:

approaching: the act of drawing spatially closer to something
closing: approaching a particular destination; a coming closer; a narrowing of a gap

Other hyponyms of approaching include access, closure, landing approach, run-up.

approaching (noun)	closing (noun)
the act of drawing spatially closer to something	termination of operations
the temporal property of becoming nearer in time	the act of closing something
the event of one object coming closer to another	a concluding action
	approaching a particular destination; a coming closer; a narrowing of a gap
	the last section of a communication

approaching (adjective)	closing (adjective)
of the relatively near future	final or ending