You're proabably wondering how all of this information relates to each other. I wondered the exact same thing when I was in your position. Well it's quite simple. They all conicide with one another in one way or another. I mean Plato hated the Sophists so that must have something to do with it. The stem of rhetoric is philosophy, when I first took this course I thought since we were learning about Plato and Socrates etc., that it was a philosophy course and I wasn't understand why we had to take it. The main components that each of the schools feed off of each other are that of truth, reality and knowledge.
First off, the whole part of this debate is whether truth is absolute, whether it creates knowledge and if it is real. Does knowledge help us shape the truth? For example, Aristotles belief that truth is attained through personal experience is like the Sophists, however, Aristotle believed that absolute truth could be attained whereas the Sophists did not believe truth to be "absolute." Another similarity between the Sophists and Aristotle was that they both divyed up the parts of a speech into three parts. For the Sophists it was the parts of the body (the head, torso, legs) and for Aristotle it was his three appeals (ethos, pathos and logos). In terms of Aristotle and Plato, they both believed in absolute truth and thought that dialect was the most important component of rhetoric.
Secondly, Plato hated the Sophists. They both believed that the other school had it wrong. Plato believed in absolute truth whereas the Sophists didn't. Plato hated rhetoric and the Sophists loved it and used it in anyway that they could. The Sophists also believed that rhetoric was something that could be taught. They both started acadmeies within their schools so that was an accomplishment.
Finally, all three of the schools were Greek (at least they had that in common) and they strove for the importance of virtues, oral communication and finding the truth, whether they believed it was absolute or probable.