There are many cases that you need to convert M4V to MOV. Though both developed by Apple, MOV format presents a lot of advantages that are quite usable to everyday use while iTunes purchased or rental M4V files are protected by DRM which causes many limitations. Besides, MOV works better and has more widespread support than M4V for streaming video. But the most typical case is for QuickTime as MOV was originally developed by Apple as a file format for its QuickTime movie player.
QuickTime & MOV
QuickTime is an extensible multimedia framework developed by Apple Inc., capable of handling various formats of digital video, picture, sound, panoramic images, and interactivity. QuickTime is available for Apple and IBM compatible users running a compatible operating system such as Microsoft Windows or any Macintosh operating system. With IBM compatible computers, QuickTime is commonly used to play .MOV extension files.
The MOV file type is primarily associated with QuickTime. It is a QuickTime media container format. Files that are saved in .MOV format are compressed, making it easier to download and stream video from the Internet to your computer or portable media device. Many of the movies and videos that are available online are distributed in .MOV format