public debate vs speaking

public debate and speaking both are nouns.

Word	Noun	Adjective	Verb	Adverb
public debate	Yes	No	No	No
speaking	Yes	Yes	No	No

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

public debate: the formal presentation of a stated proposition and the opposition to it (usually followed by a vote)
speaking: delivering an address to a public audience

Other hypernyms of public debate include oral presentation, public speaking, speechmaking.

public debate (noun)	speaking (noun)
the formal presentation of a stated proposition and the opposition to it (usually followed by a vote)	delivering an address to a public audience
	the utterance of intelligible speech

public debate (adjective)	speaking (adjective)
	capable of or involving speech or speaking
	capable of speech