hunting vs blood sport

hunting and blood sport both are nouns.

Word	Noun	Adjective	Verb	Adverb
hunting	Yes	No	No	No
blood sport	Yes	No	No	No

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

hunting: the pursuit and killing or capture of wild animals regarded as a sport
blood sport: sport that involves killing animals (especially hunting)

Other hypernyms of hunting include field sport, outdoor sport.

hunting (noun)	blood sport (noun)
the work of finding and killing or capturing animals for food or pelts	sport that involves killing animals (especially hunting)
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