Is there any meaningful difference between a "figure of speech" and a "figure of thought". Searching for a definition of "figure of thought" leads to many esoteric discussions relating to ancient rhetoric and philosophy. How can I tell a figure of speech apart from a figure of thought, and why would it be worth distinguishing between the two?
Yes they are different, although the definition and distinction my only be of interest to scholars of classical rhetoric. There are, according to this article from the University of Alberta, three figures: Figures of Word, Tropes (Figures of Speech), and Figures of Thought. All three are tools in rhetoric for conveying information.
Figures of word involve the actual construction of a sentence, including word selection, placement, and repetition.
Figures of speech are when words or phrases are used in a sense other than their literal meaning for dramatic effect. Hyperbole is a figure of speech.
Figures of thought are the styles that rhetoric can take, the way an argument is approached. A simile is a figure of thought.
They are different concepts, but not mutually exclusive. Examples of figures of thought could be figures of speech, and contain figures of word. Figure of speech is, by a wide margin, the concept that we are most familiar with. And we are familiar with specific types of all of them, including, hyperbole, paralipsis, metaphor, and allegory, but their technical classification wouldn't be of much interest to anyone outside of an academic setting.
From the start of an article discussing how best to interpret the Bible:
The biblical writers (in both OT and NT documents) made extensive use of a good many figures of speech (sometimes called figures of words) and figures of thought. The former is when the image or resemblance is confined primarily to a single word, whereas the latter might require for its expression a great many words, phrases and sentences. A metaphor, for example, would be a "figure of speech," whereas a parable would be a "figure of thought."