Analog and Digital Mixers
Mixers combine, route, and change the level of microphone and line inputs.
Powered Mixers
Powered mixers have integrated amplifiers to power passive speakers. Most have two discrete amp channels giving the ability to mix and power mains and monitors separately.
DJ
DJ mixers combine stereo line and phono sources, they use a crossfader to balance or fade between channels. Most have 1 or 2 mic inputs.