animal skin vs fur

animal skin and fur both are nouns.

Word	Noun	Adjective	Verb	Adverb
animal skin	Yes	No	No	No
fur	Yes	No	No	No

As nouns, fur is a hyponym of animal skin; that is, fur is a word with a more specific, narrower meaning than animal skin:

Other hyponyms of animal skin include lambskin, parchment, sheepskin, fell, hide, leather, pelt.

animal skin (noun)	fur (noun)
the outer covering of an animal	dense coat of fine silky hairs on mammals (e.g., cat or seal or weasel)
	a garment made of animal pelts or synthetic fur
	the dressed hairy coat of a mammal