Video (or audio, too) format that stores multiple languages in the same file, but only the parts that are different? DVDs or similar often offer different dubs of the same movie, TV show, etc. on one disk.  Storing a whole different video track (and audio track, too) for a movie seems a bit wasteful, given that the parts where nobody actually speaks (and, for that matter, when no on-screen text needs to appear in another language) don't need to be duplicated.

So, instead, why not provide the whole movie in some "canonical" language (maybe English), and then if other languages are available only store the parts of the movie that actually need to be translated, seamlessly loading them as needed?  Is there a video or audio format that does something like this (not necessarily on DVD)?
You don't need separate video tracks. All the differences are in the audio, which is a minuscule part of the overall data on a BVD. It's a simple matter for a player to select one of multiple audio tracks.