closeness vs nearness

closeness and nearness both are nouns.

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

As nouns, closeness and nearness are synonyms defined as:

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

closeness (noun)	nearness (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