To me they mean slightly different things. An impromptu speech is one you hadn't expected to make - you just decided on the spur of the moment to stand up and make the speech. An improvised speech refers to the content of the speech, and the fact that you aren't working from a script.

They can be synonyms, but in the U.S. I commonly hear "an impromptu SPEECH" and "improvised DIALOG." I agree with Su.Ki that "impromptu" carries the sense of an UNEXPECTED event. "My cousin is an amateur magician, and when asked he can always come up with an impromptu trick, using objects that happen to be in the room." "I didn't know the club was going to give me the 'Barbershopper of the Year' award, and I had to make an impromptu speech." "An amazing amount of the movie 'Dr. Strangelove' was unscripted; much of what you see on screen is Peter Sellers' improvised dialog." Here is an example in which "improvised" fits better than "impromptu." "I was scheduled to talk to the group, and I had a carefully written speech. Two minutes before I was scheduled to talk, I was shocked to discover that I had left my speech in my hotel room, so with no time to go back and get it, I delivered an improvised speech."

Why dou you write "u" instead of "you" ?