coldheartedness vs unconcern

coldheartedness and unconcern both are nouns.

Word	Noun	Adjective	Verb	Adverb
coldheartedness	Yes	No	No	No
unconcern	Yes	No	No	No

As nouns, unconcern is a hypernym of coldheartedness; that is, unconcern is a word with a broader meaning than coldheartedness:

coldheartedness (noun)	unconcern (noun)
an absence of concern for the welfare of others	the trait of remaining calm and seeming not to care; a casual lack of concern
	a feeling of lack of concern