distance vs indifference

distance and indifference both are nouns.

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

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

distance (noun)	indifference (noun)
the property created by the space between two objects or points	the trait of lacking enthusiasm for or interest in things generally
size of the gap between two places	the trait of remaining calm and seeming not to care; a casual lack of concern
indifference by personal withdrawal	unbiased impartial unconcern
a distant region	apathy demonstrated by an absence of emotional reactions
the interval between two times
a remote point in time

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