These words are applied to something said or done without special or advance preparation, as one might make a speech or perform some act on the "spur of the moment" (the meaning of extemporaneous in Latin). Extemporaneous is especially applied to an unmemorized speech given from notes or an outline: "Following the main address, someone in the audience began a heated extemporaneous discussion of the issues." Impromptu, derived from a Latin phrase meaning "in readiness," is applied to a speech given, a poem recited, or a song sung without advance notice or warning: "Although she was startled, Cissy gave an excellent impromptu talk."
Dictionary of problem words and expressions. Harry Shaw. 1975.