shooting vs firing

shooting and firing both are nouns.

Word	Noun	Adjective	Verb	Adverb
shooting	Yes	No	No	No
firing	Yes	No	No	No

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

Other hyponyms of shooting include shoot, countershot, discharge, firing off, gunfire, gunshot, headshot, shellfire, potshot.

shooting (noun)	firing (noun)
the act of firing a projectile	the act of setting something on fire
killing someone by gunfire	the termination of someone's employment (leaving them free to depart)
	the act of discharging a gun
	the act of firing weapons or artillery at an enemy