shortness of breath vs dyspnea

shortness of breath and dyspnea both are nouns.

Word	Noun	Adjective	Verb	Adverb
shortness of breath	Yes	No	No	No
dyspnea	Yes	No	No	No

As nouns, dyspnea is a hypernym of shortness of breath; that is, dyspnea is a word with a broader meaning than shortness of breath:

Other hypernyms of shortness of breath include dyspnoea.

shortness of breath (noun)	dyspnea (noun)
a dyspneic condition	difficult or labored respiration