hang on vs carry on

hang on and carry on both are verbs.

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

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

Other hypernyms of hang on include bear on, continue, preserve, uphold.

hang on (verb)	carry on (verb)
be persistent, refuse to stop	continue talking
hold the phone line open	direct the course of; manage or control
fix to; attach	misbehave badly; act in a silly or improper way
	keep or maintain in unaltered condition; cause to remain or last