catch one's breath vs pause

catch one's breath is not a noun while pause is a noun.

Word	Noun	Adjective	Verb	Adverb
catch one's breath	No	No	Yes	No
pause	Yes	No	Yes	No

As verbs, pause is a hypernym of catch one's breath; that is, pause is a word with a broader meaning than catch one's breath:

catch one's breath: take a short break from one's activities in order to relax
pause: cease an action temporarily

Other hypernyms of catch one's breath include break, intermit.

catch one's breath (noun)	pause (noun)
	temporary inactivity
	a time interval during which there is a temporary cessation of something

catch one's breath (verb)	pause (verb)
take a short break from one's activities in order to relax	cease an action temporarily
	interrupt temporarily an activity before continuing