What is the term for the use of the exact words of the speaker?

The term for the use of the exact words of the speaker is "direct quotation." This term specifically refers to quoting someone verbatim, maintaining all original wording and punctuation. Direct quotations are often used in writing to provide clear evidence of a point, demonstrate authority, or convey a message in the speaker's original voice.

In contrast, paraphrasing involves rephrasing the speaker’s ideas in one's own words, while a summary condenses the main points of a larger text into a brief overview. Dialogue refers to a conversation between characters in a narrative or play. Each of these other terms serves different functions in writing, but when aiming to reflect someone's exact words, direct quotation is the appropriate choice.