shot vs firing off

shot and firing off both are nouns.

Word	Noun	Adjective	Verb	Adverb
shot	Yes	Yes	No	No
firing off	Yes	No	No	No

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

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

shot (noun)	firing off (noun)
the act of firing a projectile	the act of discharging a gun
the act of putting a liquid into the body by means of a syringe
informal words for any attempt or effort
(sports) the act of swinging or striking at a ball with a club or racket or bat or cue or hand
the launching of a missile or spacecraft to a specified destination
an attempt to score in a game
a blow hard enough to cause injury
throwing the basketball toward the hoop
a solid missile discharged from a firearm
an informal photograph; usually made with a small hand-held camera
an explosive charge used in blasting
sports equipment consisting of a heavy metal ball used in the shot put
an estimate based on little or no information
an aggressive remark directed at a person like a missile and intended to have a telling effect
a consecutive series of pictures that constitutes a unit of action in a film
a person who shoots (usually with respect to their ability to shoot)
a small drink of liquor
a chance to do something

shot (adjective)	firing off (adjective)
varying in color when seen in different lights or from different angles