MP3 is a digital music format which allows CD tracks to be reduced to around a tenth of their normal size without a significant loss of quality. MP3 gets rid of a lot of the information recorded in a song that our ears are not able to hear and then uses complex algorithms to reduce the file size. This then enables you to get hundreds of songs on to a CD and it also has opened up a new market over the internet - the download market as download times have been significantly reduced.
The MP3 format is a lossy format. That means that an MP3 file does not contain 100% of the original audio information. Instead, MP3 files use perceptual coding. In other words, that means it removes the information that your ear doesn't notice thereby making the file smaller. The reason lossy formats are used over raw is that raw audio files are too large to travel over the internet at any great speed. By using lossy formats it enables even dial up users to download mp3 files at a reasonable speed. Raw file formats generally require 176,000 bytes per second compared to a lossy format which requires 17,600. The difference is massive and so are the download times.
The M4R is an iPhone ringtone file that is essentially a renamed AAC (m4a) file. Not all iTunes Music Store songs can be used to create M4R ringtones. In order to create an M4R ring tone from an iTunes song, the song must allow for M4R ringtone creation. An M4R ring tone is automatically transferred to a user's iPhone when the iPhone is synced with the user's computer.
M4R is essentially a renamed AAC (M4A) file - it is similar to MP3 but compresses the digital audio files further. It is part of the MPEG-4 standard and is specified in the ISO/IEC standard 14496-3. It is a lossy algorithm much like AAC and MP3. M4R supports auditory masking - essentially discarding data with minimal loss of quality.