Do you believe rhetorics and public speaking go hand in hand?

Answer 1

Certainly rhetorics come into play if you are giving a persuasive or motivational speech or debating or presenting a pitch.

And on a bit more of a subtle level, when public speaking on any topic and for any kind of speech (narrative, informative, entertaining, demonstrative, oratorical, special occasion, explanatory, or eulogy) one would be on some level persuading an audience (or proving to an audience0 that they have earned the right to be speaking on a topic, by being an authority on the topic, or via direct experience with a topic, or having studied a topic in depth.

Answer 2

I consider this to be a fact. Public speaking generally involves convincing your audience to take particular actions, and the tools necessary to pass along that conviction are part of Rhetoric, and have been for a couple of millenia at least.