What happens when there is a "movie within a movie" or a "film within a film."
It's usually just called "film-within-a-film," "movie-within-a-movie," "play-within-a-play," "play-within-a-movie," or whatever's most appropriate to the situation.  There's a french term which describes it (mise en abyme), but as an english speaker, it's often more practical just to describe the technique however it appears.  The Wikipedia entrance on story within a story gives many examples from film, theater, and literature.  The first example that comes to my mind is Nation's Pride, the film within Quentin Tarantino's Inglorious Basterds.  Personally, I would call Nation's Pride a film-within-a-film, and I think many other writers would too.