clear the throat vs cough

clear the throat is not a noun while cough is a noun.

Word	Noun	Adjective	Verb	Adverb
clear the throat	No	No	Yes	No
cough	Yes	No	Yes	No

As verbs, cough is a hypernym of clear the throat; that is, cough is a word with a broader meaning than clear the throat:

clear the throat (noun)	cough (noun)
	a sudden noisy expulsion of air from the lungs that clears the air passages; a common symptom of upper respiratory infection or bronchitis or pneumonia or tuberculosis

clear the throat (verb)	cough (verb)
clear mucus or food from one's throat	exhale abruptly, as when one has a chest cold or congestion