upper limit vs peak

upper limit and peak both are nouns.

Word	Noun	Adjective	Verb	Adverb
upper limit	Yes	No	No	No
peak	Yes	No	Yes	No

As nouns, peak is a hypernym of upper limit; that is, peak is a word with a broader meaning than upper limit:

Other hypernyms of upper limit include extremum, large indefinite amount, large indefinite quantity.

upper limit (noun)	peak (noun)
the limit on the upper (or northernmost) side of something	a brim that projects to the front to shade the eyes
the largest possible quantity	the top or extreme point of something (usually a mountain or hill)
	the highest point (of something)
	the most extreme possible amount or value
	a V shape
	the highest level or degree attainable; the highest stage of development
	the period of greatest prosperity or productivity

upper limit (verb)	peak (verb)
	to reach the highest point; attain maximum intensity, activity