hunting vs fox hunting

hunting and fox hunting both are nouns.

Word	Noun	Adjective	Verb	Adverb
hunting	Yes	No	No	No
fox hunting	Yes	No	No	No

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

hunting: the pursuit and killing or capture of wild animals regarded as a sport
fox hunting: mounted hunters follow hounds in pursuit of a fox

hunting (noun)	fox hunting (noun)
the work of finding and killing or capturing animals for food or pelts	mounted hunters follow hounds in pursuit of a fox
the pursuit and killing or capture of wild animals regarded as a sport
the activity of looking thoroughly in order to find something or someone