height vs elevation

height and elevation both are nouns.

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

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

height: elevation especially above sea level or above the earth's surface
elevation: distance of something above a reference point (such as sea level)

As nouns, height and elevation are synonyms defined as:

height and elevation: the highest level or degree attainable; the highest stage of development

Other synonyms of height include acme, meridian, peak, pinnacle, summit, superlative, tiptop, top.

height (noun)	elevation (noun)
the vertical dimension of extension; distance from the base of something to the top	the act of increasing the wealth or prestige or power or scope of something
(of a standing person) the distance from head to foot	drawing of an exterior of a structure
elevation especially above sea level or above the earth's surface	distance of something above a reference point (such as sea level)
the highest level or degree attainable; the highest stage of development	(ballet) the height of a dancer's leap or jump
	the event of something being raised upward
	a raised or elevated geological formation
	angular distance above the horizon (especially of a celestial object)
	the highest level or degree attainable; the highest stage of development