breath vs breathing in

breath and breathing in both are nouns.

Word	Noun	Adjective	Verb	Adverb
breath	Yes	No	No	No
breathing in	Yes	No	No	No

As nouns, breathing in is a hyponym of breath; that is, breathing in is a word with a more specific, narrower meaning than breath:

breath: the process of taking in and expelling air during breathing
breathing in: the act of inhaling; the drawing in of air (or other gases) as in breathing

Other hyponyms of breath include breathing out, exhalation, expiration, aspiration, inhalation, inspiration, intake.

breath (noun)	breathing in (noun)
the process of taking in and expelling air during breathing	the act of inhaling; the drawing in of air (or other gases) as in breathing
an indirect suggestion
a slight movement of the air
the air that is inhaled and exhaled in respiration
a short respite