I tried looking for samples online, but many of them are not geared towards teachers so they don't really fit your needs. They all really include many of the same things except maybe you would stress different aspects depending on the letter they're asking for.
Cover letter: elaborates slightly more the experiences in your resume.
Letter of Introduction: Introduce yourself, strengths, weaknesses, experience/education
Letter on Intent: Why do you want to work where you're applying? What could you offer the school if hired?
You would probably want to include all of those topics in all of the letters, but just stress the one that they asked for....
I think that many places just use the terms for the types of letters interchangably (sp?).