public prosecutor vs DA

public prosecutor and DA both are nouns.

Word	Noun	Adjective	Verb	Adverb
public prosecutor	Yes	No	No	No
DA	Yes	No	No	No

As nouns, DA is a hyponym of public prosecutor; that is, DA is a word with a more specific, narrower meaning than public prosecutor:

public prosecutor: a government official who conducts criminal prosecutions on behalf of the state
DA: an official prosecutor for a judicial district

Other hyponyms of public prosecutor include district attorney, state's attorney, state attorney.

public prosecutor (noun)	DA (noun)
a government official who conducts criminal prosecutions on behalf of the state	an official prosecutor for a judicial district