Isn’t there a difference between an animal’s coat and an animal’s fur?
Yes, they can take off their coat and hang it up in the cupboard when they get home. They cannot, of course, remove their fur.
Coat can include the health of the skin the fur is attached to. It depends on who's using the word and in what manner.
L. E. Gant: Animals don't wear clothes (normally)
Animals don't wear clothes (normally) :-) However, "fur" is where we take the skin and use it after tanning and curing, while "coat" is where we don't. So, a bear or tiger has fur, while sheep and apacas have coats (we shear the animals to get "wool")