Classical Rhetoric got its start in ancient Greece, circa 6th century BC and the Romans built upon it. It remained ascendant through the 1920s or at any rate it was supplanted in most schools in the United States in the 1920s by Communications Studies. A lot of things changed in American education around that time; Classical Rhetoric was not the only subject affected. Statesman Debate recognizes the superior worth of Classical Rhetoric and relies heavily upon it for its public speaking and forensics training.
What sets Classical Rhetoric apart from other approaches is paradoxically both its rigor and labor saving devices. It stresses argumentation and takes the approach that delivery is, at root, a byproduct of having something worthy saying. Also the adage–do things right the first time–animates the classical rhetorician. Toward the end of getting it right from the start, the student of this technique is very deliberate at the onset. This is where he or she follows a tried-and-proven protocol, which, in turn, saves much time in the long run and maximizes the chances of successful persuasion.
Communication Studies, which is commonplace nowadays, may in the hands of some instructors match the longer established curriculum. Sometimes the former is not as concerned with argumentation, and places greater emphasis upon delivery and social media. There is this concern that the Communications student specializes too quickly, in say, journalism or public relations, and does not spend sufficient time laying the broad foundation in argumentation.
Social media and delivery are by no means neglected in our own training, but Classical Rhetoric is king, as far as we are concerned.
One of the beautiful nuances of Classical Rhetoric, which may have no or limited counterpart in Communication Studies, is the dichotomy between routine-situation and crisis speeches.
The photo of the Roman Senate is public domain, care of Phaeselis Wiki.