public discussion vs discussion

public discussion and discussion both are nouns.

Word	Noun	Adjective	Verb	Adverb
public discussion	Yes	No	No	No
discussion	Yes	No	No	No

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

public discussion: free and open discussion of (or debate on) some question of public interest
discussion: an exchange of views on some topic

Other hypernyms of public discussion include give-and-take, word.

public discussion (noun)	discussion (noun)
free and open discussion of (or debate on) some question of public interest	an exchange of views on some topic
	an extended communication (often interactive) dealing with some particular topic