Headphones are a dime a dozen, but not all of them are suitable for studio work. Generally speaking, open headphones are more suitable for listening to and mixing music, while closed headphones are used for isolation and thus fall into the category of recording and DJing. This is because with open headphones, sound leaks out and may also get onto the recording.
In addition, the monitor mix should not be affected by external noises such as loud amps or the drums during the rehearsal. In terms of sound, it often comes in handy to pay attention to a reasonable high-midrange reproduction so that the musician can easily locate themselves and their colleagues. When DJing, on the other hand, the bass is clearly in the foreground.
Studio Headphones used for mixing should have a sound that is as neutral as possible and should not have any emphasis/cutting in the frequency range, otherwise serious errors can occur during mixing.
HiFi Headphones on the other hand, are designed to give the wearer the most unrestricted listening pleasure possible. For this reason, the frequency response is never linear, but works with boosts in the bass and treble range - the famous bathtub. In addition, the outer treble range is often attenuated so that noise and artifacts, e.g. from MP3s, can be more easily ignored.
As with almost every device, headphones have their own amplifiers. Music listeners usually have the choice between the internal headphone amplifier of their stereo system or computer and an external solution. The advantage of an external headphone amplifier is the immensely improved sound quality of higher-priced devices, often numerous connection options to e.g. turntables or CD decks or even several outputs with their own volume control. Such devices are also used in the rehearsal room or studio, for example, to send the monitor mix from the mixing console to the musician's ears.