Direct speech refers to quoting someone's exact words, while indirect speech involves reporting what someone said without using their exact words. The key differences are that indirect speech changes pronouns, adverbs of time and place, and verb tenses. For example, direct speech would be "I am working for my country" while the indirect version reported by Anderson Cooper would be "He said that he was working for his country." The document provides additional examples of how direct speech converts to indirect speech by changing verb tenses and other elements.