Final answer:
A soliloquy is an individual's inner reflections shared with the audience, while a dramatic monologue is a lengthy speech addressed to characters or the audience in a play.
Explanation:
A soliloquy is an extended dramatic passage where a character gives their speech alone on stage, expressing inner thoughts and feelings to the audience. On the other hand, a dramatic monologue is a lengthy speech by a single character often seen in plays, such as Robert Browning's "My Last Duchess." The distinction between the two lies in who the speech is addressing - an audience or other characters.
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