The distinction here is that a (regular) insert song plays during the show as part of the soundtrack. The characters inside the show are not aware that any music is playing at that point. Here however the song is part of the plot itself. I think that's what 劇中 is emphasizing.
It's similar to the parts of the Disney movies, where the scene turns into some sort of musical for a a short amount of time (Hakuna Matata e.g.).
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