extremity vs limb

extremity and limb both are nouns.

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

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

extremity: an external body part that projects from the body
limb: one of the jointed appendages of an animal used for locomotion or grasping: arm, leg, wing, flipper

Other hyponyms of extremity include chelicera, mouthpart, fang, chela, claw, nipper, pincer, parapodium, fin, pleopod, swimmeret, dactyl, digit.

extremity (noun)	limb (noun)
an external body part that projects from the body	any projection that is thought to resemble a human arm
that part of a limb that is farthest from the torso	the graduated arc that is attached to an instrument for measuring angles
the outermost or farthest region or point	either of the two halves of a bow from handle to tip
the greatest or utmost degree	one of the jointed appendages of an animal used for locomotion or grasping: arm, leg, wing, flipper
an extreme condition or state (especially of adversity or disease)	(astronomy) the circumferential edge of the apparent disc of the sun or the moon or a planet
	any of the main branches arising from the trunk or a bough of a tree