extremum vs lower limit

extremum and lower limit both are nouns.

Word	Noun	Adjective	Verb	Adverb
extremum	Yes	No	No	No
lower limit	Yes	No	No	No

As nouns, lower limit is a hyponym of extremum; that is, lower limit is a word with a more specific, narrower meaning than extremum:

Other hyponyms of extremum include minimum, maximum, upper limit.

extremum (noun)	lower limit (noun)
the point located farthest from the middle of something	the limit on the lower (or southernmost) side of something
the most extreme possible amount or value	the smallest possible quantity