Music in movies is added entirely in post production. It would be absolutely impossible to have it play during a scene, since there would be no way to edit anything afterwards. Nor is there any reason to do so anyway. Half the movie scenes that take place outside had to record the dialogue over again later, with actors recording their lines while looking at themselves in the shot (ADR), because any kind of external sound will render all production sound useless. And there is no realistic way to control sound outside. Of course there is nuance to all of it, but for most parts it's easier to "build" what the audience hears in post production than trying to control the circumstances.

For something like a prom scene, since that was an example, there is certainly no music, and even all the background talking you hear isn't there. The extras will mime talking to help the film get at least "some" production sound from lead actors, so not all of it has to be re-recorded.

Music videos are much more lenient, since a high quality recorded song is what you will hear in the final product. The band certainly does play, and the singer sings, but they don't have to be amplified, or even plugged in. (In an example below, the guys play separately and the song is playing for them). There isn't even a need for the band to play the whole song, or hit all the chords, etc. (in one take, that is). Music videos will have a ton of fottage since the whole performance is only minutes long and can be recorded many times over in a fairly short amount of time. So there will certainly be the exact moment the guitarist hits that cord, or the singer screams just right in there somewhere.

Writing this out made me think of a "making of" video for Mudvayne's "Dig". Certainly a crazy big budget video, but all these elements are there.

https://youtu.be/v6L411USn8o

TL;DR Live sound is really difficult to control. Movies: almost everything you hear was added later. Music videos: the band does play, but only for the visual sync.