Video mixers take inputs from several analog video sources and produce a single output signal, usually with the ability to do fades and picture-in-picture. These devices are also referred to as production switchers.
For analog production, switchers should support picture-in-picture, rather than just digital wipe and fade effects. For network production, instructor, overhead camera, slides are sent as separate streams (or possibly mixed digitally).
For good video quality, one cannot simply split a video signal via a simple splitter cable, particularly when longer cable lengths are involved. Distribution amplifiers take a video input and distribute it, via amplifiers, to two to five video outputs. Some distribution amplifiers also convert the signal from Y/C (S-Video) to composite (RCA) or vice versa.
One can display S-Video and composite video on a VGA monitor with a converter.
Conversely, tools such as Epiphan VGA2USB allow the conversion of VGA output to video input