Cue mix
A separate mix fed to the musicians' headphones while they record, independent of what the engineer is listening to.
The drummer wants more bass, the singer wants more of themselves, and neither wants to hear the engineer's tweaks. So cue mixes are built from aux sends tapped pre-fader: the engineer can mix freely without anything changing in the headphones. A larger console can feed four or six of these at once, each to its own headphone amp.
From the 2000s onwards, personal mixers at each player's position became common, receiving every channel over a network and letting the musician do the adjusting. It saves the engineer time and ensures everyone eventually hears only themselves. In a DAW setup, latency is a separate problem, which is what direct monitoring solves.