Original: International trailers use the Die Hard 4.0 title, as the film was released outside North America with that title. Early into the DVD commentary for the film, both Wiseman and Willis note a preference for Die Hard 4.0, and subtly mock the Live Free or Die Hard title.
Simplified: Live Free or Die Hard (also called Die Hard 4.0 outside of North America) is an action movie starring Bruce Willis and Justin Long.