obstinate vs hold on

obstinate is an adjective but hold on is not an adjective.

Word	Noun	Adjective	Verb	Adverb
obstinate	No	Yes	Yes	No
hold on	No	No	Yes	No

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

Other hypernyms of obstinate include hang in, hang on, persevere, persist.

obstinate (adjective)	hold on (adjective)
tenaciously unwilling or marked by tenacious unwillingness to yield
resistant to guidance or discipline
stubbornly persistent in wrongdoing

obstinate (verb)	hold on (verb)
persist stubbornly	be persistent, refuse to stop
	stop and wait, as if awaiting further instructions or developments
	hold the phone line open
	hold firmly
	retain possession of