horse fancier vs animal fancier

horse fancier and animal fancier both are nouns.

Word	Noun	Adjective	Verb	Adverb
horse fancier	Yes	No	No	No
animal fancier	Yes	No	No	No

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

horse fancier (noun)	animal fancier (noun)
a person who breeds and cares for horses	a person who owns, shows, judges, or breeds animals