MOV and AVI are nothing to do with any "status" of a movie. They are file extensions. They are automatically generated by the software that was used to create them, and exist to instruct your computer which software to use to play them.
Quicktime is generally the software used to play .MOV files. They are the native files created by the iPhone and iPad.
I suggest using VLC for playing movies. So long as you keep it more or less up to date, it will play just about any movie, without you having to bother looking for codecs. (Codecs are software patches which allow a program to play files which are not native to it.) You also won't have to worry about converting files from one type to another.
You can download VLC free from
http://www.videolan.org/vlc/
There is a version available from the Apple App Store for mobile devices, but I can't vouch for it since I've never used the current version.