height vs level

height and level both are nouns.

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

As nouns, level is a hyponym of height; that is, level is a word with a more specific, narrower meaning than height:

Other hyponyms of height include ceiling, ceiling.

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

height: the highest level or degree attainable; the highest stage of development
level: a specific identifiable position in a continuum or series or especially in a process

Other hypernyms of height include degree, point, stage.

height (noun)	level (noun)
the vertical dimension of extension; distance from the base of something to the top	indicator that establishes the horizontal when a bubble is centered in a tube of liquid
(of a standing person) the distance from head to foot	a structure consisting of a room or set of rooms at a single position along a vertical scale
elevation especially above sea level or above the earth's surface	a flat surface at right angles to a plumb line
the highest level or degree attainable; the highest stage of development	a position on a scale of intensity or amount or quality
	height above ground
	an abstract place usually conceived as having depth
	a specific identifiable position in a continuum or series or especially in a process
	a relative position or degree of value in a graded group

height (adjective)	level (adjective)
	of the score in a contest
	being on a precise horizontal plane
	not showing abrupt variations
	having a surface without slope, tilt in which no part is higher or lower than another
	oriented at right angles to the plumb

height (verb)	level (verb)
	become level or even
	talk frankly with; lay it on the line
	direct into a position for use
	aim at
	make level or straight
	tear down so as to make flat with the ground