bad hat vs persona non grata

bad hat and persona non grata both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad hat	Yes	No	No	No
persona non grata	Yes	No	No	No

As nouns, persona non grata is a hypernym of bad hat; that is, persona non grata is a word with a broader meaning than bad hat:

Other hypernyms of bad hat include unwelcome person.

bad hat (noun)	persona non grata (noun)
someone who deliberately stirs up trouble	a person who for some reason is not wanted or welcome
	a diplomat who is unacceptable to the government to which he is sent