I am not an expert, but I'll try my best to explain what's out there.
In America, I think the most popular is CD+G. Known as CD+Graphics. It's like a CD audio with graphics embedded into the CD, but no video. You'll need special CD player that can handle the graphics and output to TV. There are program on the computer that can also play those CD.
The VCD you are talking about in Asia is basically music video Karaoke. With vocal recorded of the left or right channel. You don't need 2 set of speakers. You you need to do is select which channel you want the audio to play. Also, a lot of software can do that. There are also VCD player out there.
Next is DVD. Music video karaoke record in DVD. Vocal and nonvocal is recorded as separate tracks. So, you get true stereo without losing quality. You also get a higher quality video. Except when some company try to put too much video it become overly compressed. There's also software that allows you to choose the track to play and a lot of karaoke player let you change the track.
There are machine out there called MIDI-Karaoke player. It's a player that has about 20,000 songs with about 1 hours of video that loop over and over while the song overlay on top of the video. You use the remote to choose the song, reserve, play and all that stuff.
On the computer, there are MIDI (.kar) karaoke. Most people don't use this anymore because the audio quality isn't that great. MP3+G, this is similar to CD+G except the audio is in MP3 and the lyric is in graphic. MP3+.lrc, this is MP3 with matching lyric file. The program will load and display the text for the MP3 while playing.
Ok, I think that's all I can explain. If I explain it wrong, please let me know.
By the way, I just finish writing a karaoke software player. It doesn't have all the feature I want in it yet so I am still not making it version 1. It allow you to play MP3+.lrc and .kar files. You can record your own video and use it as the background. You can even use the camera and have the text playing on top of it live. You can get it here at
http://www.walasoft.com/walaoke