nearness vs proximity

nearness and proximity both are nouns.

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

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

Other hyponyms of nearness include propinquity, adjacency, contiguity, contiguousness, localness.

nearness (noun)	proximity (noun)
the spatial property resulting from a relatively small distance	the property of being close together
	a Gestalt principle of organization holding that (other things being equal) objects or events that are near to one another (in space or time) are perceived as belonging together as a unit
	the region close around a person or thing