MP4

MPEG-4 Part 14, formally ISO/IEC 14496-14:2003, is a multimedia container format standard specified as a part of MPEG-4. It is most commonly used to store digital audio and digital video streams, especially those defined by MPEG, but can also be used to store other data such as subtitles and still images. Like most modern container formats, MPEG-4 Part 14 allows streaming over the Internet. The official filename extension for MPEG-4 Part 14 files is .mp4, thus the container format is often referred to simply as MP4. Note that many devices advertised as "MP4 players" are simply AMV video capable MP3 players, and do not play MPEG-4 part 14 or any other MPEG-4 format. MPEG-4 Part 14 was based on Apple's QuickTime container format. MPEG-4 Part 14 is essentially identical to the QuickTime MOV format, but formally specifies support for Initial Object Descriptors (IOD) and other MPEG features. 

.MP4 versus .M4A file extensions
The existence of two different file extensions for naming audio-only MP4 files has been a source of confusion among users and multimedia playback software. Since MPEG-4 Part 14 is a container format, MPEG-4 files may contain any number of audio, video, and even subtitle streams, making it impossible to determine the type of streams in an MPEG-4 file based on its filename extension alone. In response, Apple Inc. started using and popularizing the .m4a file extension. Software capable of audio/video playback should recognize files with either .m4a or .mp4 file extensions, as would be expected, as there are no file format differences between the two. Most software capable of creating MPEG-4 audio will allow the user to choose the filename extension of the created MPEG-4 files

The .m4p is usually used as the music format for the iTunes Store DRM copy protected content, while .m4a is now being used by the iTunes Store for DRM-free, unprotected music files and as an export option in QuickTime Pro.