Mix - is the process of blending all the individual tracks in a recording to create a version of the song that sounds as good as possible – the “mix”. The process can include: Balancing the levels of the tracks that have been recorded. Fine-tuning the sound of each instrument or voice using equalisation (EQ).
Remix -A piece of media which has been altered from its original state by adding, removing, and/or changing pieces of the item. A song, piece of artwork, book, video, or photograph can all be remixes. The only characteristic of a remix is that it appropriates and changes other materials to create something new.
Original Mix -a piece of media that has not been modified from its’ first inception.
Extended Mix - a piece of media that has been altered by adding additional content to the original mix.
Edit - (there are many types of edits in music, this is for radio) In music, a radio edit is a modification, typically truncated, intended to make a song more suitable for airplay, whether it be adjusted for length, profanity, subject matter, instrumentation, or form. Radio edits may also be used for commercial single versions, which may be denoted as the 7" version.
Version - (there are many types of version in music. Not sure what you're asking) a version, just like any other artistic medium, represents a current form and/or release. There are many types ranging from (cover, original, edited, single, VIP, etc)
Bootleg - is an audio or video recording of a performance that was not officially released by the artist or under other legal authority. The process of making and distributing such recordings is known as bootlegging.
Mashup - is a song or composition created by blending two or more pre-recorded songs, usually by overlaying the vocal track of one song seamlessly over the instrumental track of another.
Medley - is a piece composed from parts of existing pieces, usually three, played one after another, sometimes overlapping. They are common in popular music, and most medleys are songs rather than instrumental.