extremity vs extreme

extremity and extreme both are nouns.

Word	Noun	Adjective	Verb	Adverb
extremity	Yes	No	No	No
extreme	Yes	Yes	No	No

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

Other hyponyms of extremity include bound, boundary, bounds, end, terminal, extreme point, extremum, limit.

extremity (noun)	extreme (noun)
an external body part that projects from the body	the furthest or highest degree of something
that part of a limb that is farthest from the torso	the point located farthest from the middle of something
the outermost or farthest region or point
the greatest or utmost degree
an extreme condition or state (especially of adversity or disease)

extremity (adjective)	extreme (adjective)
	most distant in any direction
	far beyond a norm in quantity or amount or degree; to an utmost degree
	of the greatest possible degree or extent or intensity
	beyond a norm in views or actions