Video playback on computers is a very murky world and having an old PPC adds a bit more difficulty due to the hardware.
For playback in Quicktime, install Perian:
http://www.perian.org/
This is a pack of codecs that Quicktime can use to open formats that are not native to it - it's pretty comprehensive and tackles most things.
However, it may come as a surprise but Quicktime, despite being Apple software, is not the best video player for PPC Macs - VLC is much better - more efficent and readily tackles video files Quicktime can't.
For Tiger you'll need version 0.9.10:
http://download.videolan.org/pub/videolan/vlc/0.9.10/macosx/
I've found the best player to be XBMC (version 11 for PPC), however this is a media centre rather than a simple file player but it does appear to have the most powerful player engine.
The difference between MPEG-4 and MP4 in your case will be the codec in the file - essentially how the video file is stored and played back - it's likely the MPEG-4 file was using a codec your Powerbook didn't have hence the green screen.
Bear in mind that video files available online now use codecs that weren't mainstream when the Powerbook was made, so are either unplayable or difficult to play on it - however, if you're patient there are plenty of tools available to convert video into more agreeable formats that fly on PPC.