public press vs print media

public press and print media both are nouns.

Word	Noun	Adjective	Verb	Adverb
public press	Yes	No	No	No
print media	Yes	No	No	No

As nouns, print media is a hypernym of public press; that is, print media is a word with a broader meaning than public press:

public press: the print media responsible for gathering and publishing news in the form of newspapers or magazines
print media: a medium that disseminates printed matter

public press (noun)	print media (noun)
the print media responsible for gathering and publishing news in the form of newspapers or magazines	a medium that disseminates printed matter