fox hunting vs hunting

fox hunting and hunting both are nouns.

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

As nouns, hunting is a hypernym of fox hunting; that is, hunting is a word with a broader meaning than fox hunting:

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

Other hypernyms of fox hunting include hunt.

fox hunting (noun)	hunting (noun)
mounted hunters follow hounds in pursuit of a fox	the work of finding and killing or capturing animals for food or pelts
	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