A DJ, or disc jockey, is a person who selects and plays recorded music for an audience, typically at a party, dance club, or radio broadcast. They may use various tricks and techniques to make the transitions between songs smooth and entertaining.
A mixer, on the other hand, is a device used by DJs to adjust the volume, frequency, and other aspects of multiple audio signals before mixing them together into a single output. It usually has multiple input channels, each with its own level control and equalizer, as well as various features for creating crossfades and other effects.
So, in short, a DJ is a person who plays and mixes music for an audience, while a mixer is a tool that they use to do so.