extremity vs ultimacy

extremity and ultimacy both are nouns.

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

As nouns, ultimacy is a hypernym of extremity; that is, ultimacy is a word with a broader meaning than extremity:

extremity: the greatest or utmost degree
ultimacy: the state or degree of being ultimate; the final or most extreme in degree or size or time or distance

Other hypernyms of extremity include ultimateness.

extremity (noun)	ultimacy (noun)
an external body part that projects from the body	the state or degree of being ultimate; the final or most extreme in degree or size or time or distance
that part of a limb that is farthest from the torso
the outermost or farthest region or point
the greatest or utmost degree
an extreme condition or state (especially of adversity or disease)