firing vs firing off

firing and firing off both are nouns.

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

As nouns, firing and firing off are synonyms defined as:

Other synonyms of firing include discharge.

firing (noun)	firing off (noun)
the act of setting something on fire	the act of discharging a gun
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