hunting vs deer hunt

hunting and deer hunt both are nouns.

Word	Noun	Adjective	Verb	Adverb
hunting	Yes	No	No	No
deer hunt	Yes	No	No	No

As nouns, deer hunt is a hyponym of hunting; that is, deer hunt 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
deer hunt: hunting deer

hunting (noun)	deer hunt (noun)
the work of finding and killing or capturing animals for food or pelts	hunting deer
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