MP4s are mostly video that can be loaded onto PSP and mobile phones to view. Most mobile phones use the 3gp file format but many can read the mp4 format as is without conversion. My LG VX9800 has 7 episodes of the Simpsons and the "Still Seeing Breen" music video on it in mp4 format.
Files in .m4a format are actually the audio layer of (non-video) MPEG 4.
When these files have digital rights management (DRM) restrictions applied to them, their extension are often changed to .m4p, the p standing for protected. Music files purchased from the iTunes Music Store, for example, have this extension.