sigh vs respire

sigh is a noun but respire is not a noun.

Word	Noun	Adjective	Verb	Adverb
sigh	Yes	No	Yes	No
respire	No	No	Yes	No

As verbs, respire is a hypernym of sigh; that is, respire is a word with a broader meaning than sigh:

Other hypernyms of sigh include breathe, suspire, take a breath.

sigh (noun)	respire (noun)
an utterance made by exhaling audibly
a sound like a person sighing

sigh (verb)	respire (verb)
heave or utter a sigh; breathe deeply and heavily	draw air into, and expel out of, the lungs
utter with a sigh	undergo the biomedical and metabolic processes of respiration by taking up oxygen and producing carbon monoxide
	breathe easily again, as after exertion or anxiety