togetherness vs closeness

togetherness and closeness both are nouns.

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

As nouns, closeness is a hypernym of togetherness; that is, closeness is a word with a broader meaning than togetherness:

Other hypernyms of togetherness include intimacy.

togetherness (noun)	closeness (noun)
affectionate closeness	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