pacing vs gait

pacing and gait both are nouns.

Word	Noun	Adjective	Verb	Adverb
pacing	Yes	No	No	No
gait	Yes	No	No	No

As nouns, gait is a hypernym of pacing; that is, gait is a word with a broader meaning than pacing:

pacing (noun)	gait (noun)
walking with slow regular strides	a person's manner of walking
(music) the speed at which a composition is to be played	a horse's manner of moving
	the rate of moving (especially walking or running)