prosecuting attorney vs DA

prosecuting attorney and DA both are nouns.

Word	Noun	Adjective	Verb	Adverb
prosecuting attorney	Yes	No	No	No
DA	Yes	No	No	No

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

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

Other hyponyms of prosecuting attorney include district attorney, state's attorney, state attorney.

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