nearness vs closeness

nearness and closeness both are nouns.

Word	Noun	Adjective	Verb	Adverb
nearness	Yes	No	No	No
closeness	Yes	No	No	No

As nouns, nearness and closeness are synonyms defined as:

nearness and closeness: the spatial property resulting from a relatively small distance

nearness (noun)	closeness (noun)
the spatial property resulting from a relatively small distance	the spatial property resulting from a relatively small distance
	characterized by a lack of openness (especially about one's actions or purposes)
	the quality of being close and poorly ventilated
	close or warm friendship
	extreme stinginess
	a feeling of being intimate and belonging together