Broadcast Music Mixing
Most larger shows will have at least the FOH mixer and the Monitor mixer. However, if that same show is being mixed for broadcast, then there will be a third audio position located backstage or in a truck outside. This position is called the "Broadcast Music Mixer"
The broadcast music mixer is also mixing the live show simultaneously like the FOH and Monitor mixer. Their focus, however, is completely different. The broadcast music mixer's focus is to make the show sound "right" on a TV or radio speaker.
At this point, one may ask "but doesn't the FOH mixer provide the sound for TV?". On occasion, yes, this may happen, but it is not preferred. Since the FOH mixer's job is to provide sound for the audience, their mix is influenced by the venue. So they may leave certain elements of the mix out or lower because the room may naturally be aiding those elements. A broadcast mixer will isolate themselves in a quieter environment backstage that allows them to hear the finite details of the mix and ensure the representation of the show the TV audience receives is similar to that provided to the in-house audience.