highness vs height

highness and height both are nouns.

Word	Noun	Adjective	Verb	Adverb
highness	Yes	No	No	No
height	Yes	No	No	No

As nouns, height is a hypernym of highness; that is, height is a word with a broader meaning than highness:

highness: the quality of being high or lofty
height: the vertical dimension of extension; distance from the base of something to the top

Other hypernyms of highness include tallness.

highness (noun)	height (noun)
the quality of being high or lofty	the vertical dimension of extension; distance from the base of something to the top
a high degree (of amount or force etc.)	(of a standing person) the distance from head to foot
	elevation especially above sea level or above the earth's surface
	the highest level or degree attainable; the highest stage of development