Eloquence is an artistic, flowing, and often beautiful form of expression, coming from the Latin for 'to speak out'. One has the sense of words flowing out naturally. It may be persuasive, but naturally so, and you will tend to want to listen to it!
Eloquence tends also to come from the heart, often conveying a passionate and deeply-held conviction of the speaker, and this emotion behind the words gives eloquence a sense of truth and sincerity that can be missing from rhetoric.
Eloquence often also conveys even a complex concept in just a few words - whereas rhetoric might use many mords to do the same thing.
Rhetoric is a more mental form of communication, putting forward arguments and reason - often wanting to make a point, or several points - often in order to win an argument, or 'win you over', as in politics.
Rhetoric's clever use of language may be designed to persuade - but it is not necessarily flowing, and not necessarily beautiful - unless the speaker also happens to be - eloquent!
Rhetoric is quite often described as 'empty rhetoric' - meaning that the speaker is constructing clever arguments, or perhaps making complex verbal constructions - but that these lack authenticity and may in fact not be entirely genuine or even true.
Examples of eloquence:
"In a word, to feel your subject thoroughly, and to speak without fear, are the only rules of eloquence." (Oliver Goldsmith)
Ordinary riches can be stolen; real riches cannot. In your soul are infinitely precious things that cannot be taken from you. (Oscar Wilde)
Given a place to do your work, a little job to do, you can quite easily sew for your soul the fulfilment that it seeks
Example of rhetoric:
- We in Britain are rightly proud of the way in which, since Magna Carta in the year 1215, we have pioneered and developed representative institutions to stand as bastions of freedom. And proud too of the way in which for centuries Britain was a home for people from the rest of Europe who sought sanctuary from tyranny. (Margaret Thatcher)
The real difference is perhaps that with eloquence, you are waiting for them to go on, and with rhetoric, you are often dying for them to stop...