PHS vs federal agency

PHS and federal agency both are nouns.

Word	Noun	Adjective	Verb	Adverb
PHS	Yes	No	No	No
federal agency	Yes	No	No	No

As nouns, federal agency is a hypernym of PHS; that is, federal agency is a word with a broader meaning than PHS:

PHS: an agency that serves as the office of Surgeon General; includes agencies whose mission is to improve the public health
federal agency: an administrative unit of government

Other hypernyms of PHS include agency, authority, bureau, government agency, office.

PHS (noun)	federal agency (noun)
an agency that serves as the office of Surgeon General; includes agencies whose mission is to improve the public health	an administrative unit of government