cowpox vs animal disease

cowpox and animal disease both are nouns.

Word	Noun	Adjective	Verb	Adverb
cowpox	Yes	No	No	No
animal disease	Yes	No	No	No

As nouns, animal disease is a hypernym of cowpox; that is, animal disease is a word with a broader meaning than cowpox:

cowpox: a viral disease of cattle causing a mild skin disease affecting the udder; formerly used to inoculate humans against smallpox
animal disease: a disease that typically does not affect human beings

Other hypernyms of cowpox include pox.

cowpox (noun)	animal disease (noun)
a viral disease of cattle causing a mild skin disease affecting the udder; formerly used to inoculate humans against smallpox	a disease that typically does not affect human beings