DJ Mixers are a type of audio mixing console used by Disc jockeys (DJs) to control and manipulate multiple audio signals from various sources. Those sources are typically record turntables, compact cassettes, CDJs, or DJ software on a laptop. DJ mixers allow the DJ to use headphones to preview the next song before playing it to the audience through the speakers.

Is there a difference between DJ mixers and PA mixers? Are they interchangeable?
A PA mixer and DJ mixer are different and used for different purposes. Although a DJ can use a DJ mixer and  PA mixer, the latter is generally used for controlling the sound level on a PA system. A DJ mixer, however, has features commonly used by DJs like crossfading, BPM detection, headphone cues and FX capabilities, and are paired or combined with CDJs and Vinyl or media players.

What is the difference between DJ mixers and controllers?
A DJ controller is typically an all-in-one package that features transport controls for the decks, volume, speed, and EQs. A DJ mixer is a dedicated suite for mixing, and takes inputs from separate devices like CDJs, media players, vinyl players or output from an audio interface connected to a computer running a DJ software.