nearness vs distance

nearness and distance both are nouns.

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

As nouns, distance is a hypernym of nearness; that is, distance is a word with a broader meaning than nearness:

nearness (noun)	distance (noun)
the spatial property resulting from a relatively small distance	the property created by the space between two objects or points
	size of the gap between two places
	indifference by personal withdrawal
	a distant region
	the interval between two times
	a remote point in time

nearness (verb)	distance (verb)
	go far ahead of
	keep at a distance