hang on vs wait

hang on is not a noun while wait is a noun.

Word	Noun	Adjective	Verb	Adverb
hang on	No	No	Yes	No
wait	Yes	No	Yes	No

As verbs, wait is a hypernym of hang on; that is, wait is a word with a broader meaning than hang on:

Other hypernyms of hang on include await, expect, look.

hang on (noun)	wait (noun)
	the act of waiting (remaining inactive in one place while expecting something)
	time during which some action is awaited

hang on (verb)	wait (verb)
be persistent, refuse to stop	look forward to the probable occurrence of
hold the phone line open	serve as a waiter or waitress in a restaurant
fix to; attach	stay in one place and anticipate or expect something
	wait before acting