hold the line vs hold on

hold the line and hold on both are verbs.

Word	Noun	Adjective	Verb	Adverb
hold the line	No	No	Yes	No
hold on	No	No	Yes	No

As verbs, hold the line and hold on are synonyms defined as:

Other synonyms of hold the line include hang on.

hold the line (verb)	hold on (verb)
hold the phone line open	be persistent, refuse to stop
hold the line on prices; keep the price of something constant	stop and wait, as if awaiting further instructions or developments
	hold the phone line open
	hold firmly
	retain possession of