Rhetoric is closely connected to Sophism and Sophistry
Rhetoric is usually described as an art of persuading (some audience about something). It is not particularly interested with truth, only with appearance of it. Rhetoric appeals not only to the reason, but much more to the emotions. In this regards, rhetoric is close to the psychology - many good rhetoricians used psychological tricks to make their public believe in something.
The first teachers of rhetoric were the Sophists. The Sophists had a curious philosophical outlook - they believed that for every argument there can be made a counter argument, and that there is no objective independent truth, morals etc ... The famous saying by Protagoras "Man is the measure of all things" is usually interpreted as exactly this: repudiation of universal truth. This moral relativism of Sophists was famously criticized by ancient philosophers like Plato, especially since Sophists made a living by teaching wealthy students how to make arguments pro et contra concerning various topics, and not trying to establish what is true (since they did believe that is individual). As a philosophical movement, Sophism was not very fruitful, for obvious reason. Still , they have left us with the art of rhetoric, just like Plato's student Aristotle left us with logic to discern truth trough Sophism.