In Music-theatre
As with film, the term "diegetic" refers to the function of the music within a work's theatrical narrative, with particular relevance to the role of song. Within the typical format of opera/operetta, characters are not "aware" that they are singing. This is a non-diegetic use of song. If however the song is presented as a musical occurrence within the plot, then the number may be described as "diegetic".
For example, in The Sound of Music, the song "Do-Re-Mi" is diegetic, since the characters are aware they are singing. The character Maria is using the song to teach the children how to sing. It exists within the narrative sphere of the characters. In contrast, the song "How Do You Solve A Problem Like Maria?" is non-diegetic, since the musical material exists external to the narrative.
In both the 1936 and the 1951 film versions of Show Boat, as well as in the original stage version, the song "Bill" is diegetic. The character Julie LaVerne sings it during a rehearsal in a nightclub. A solo piano (played onscreen) accompanies her, and the film's offscreen orchestra (presumably not heard by the characters) sneaks in for the second verse of the song. Julie's other song in the film, "Can't Help Lovin' Dat Man" is also diegetic. In the 1936 film, it is supposed to be an old folk song known only to blacks; in the 1951 film it is merely a song which Julie knows; however, she and the captain's daughter Magnolia are fully aware that Julie is singing. When Julie, Queenie, and the black chorus sing the second chorus of the song in the 1936 version, they are presumably unaware of any orchestral accompaniment, but in the 1951 film, when Magnolia sings and dances this same chorus, she does so to the accompaniment of two deckhands on the boat playing a banjo and a harmonica, respectively. Two other songs in the 1936 Show Boat are also diegetic, "Goodbye My Lady Love" (sung by the comic dancers Ellie and Frank), and "After the Ball", sung by Magnolia. Both are interpolated into the film, and both are performed in the same nightclub in which Julie sings Bill.
The "Once More, with Feeling" episode of Buffy the Vampire Slayer toys with the concept of non-diegetic versus diegetic music when the characters find themselves compelled to burst into song in the style of a musical. The audience's first critical assumption—that this is a "musical episode" where the Buffy cast is presumably unaware that they are singing — is overturned when it becomes clear that the characters are all too aware of their musical interludes and that determining the supernatural causes for the singing will be the focus of the episode's story. The audience is then forced to abandon one form of suspension of disbelief (i.e. that musical numbers will go unacknowledged by the characters in a musical) in favour of another (that the characters are aware of how unnatural spontaneous singing is in the context of the "real world").
Read more about this topic: Diegesis