As a side note, remaster has been a term coined by the music or movie industry to describe a process where you grab the old unmastered or mastered tapes / files of a movie or a song and go through the process of mastering them again. In music, which I'm more intimate with, the production process it's usually something like:
- Music is recorded by an artist or band in the form of individual tracks per instrument
- Music is mixed by the sound engineer which then usually requires a master (some bands opt to not master their music)
- Music is mastered by the mastering engineer
A remaster either grabs the product produced by the sound engineer and goes through the process of mastering it again, or grabs the product produced by the mastering engineer and applies a new master on it (increased audio levels, more compression, added reverb, new EQ, etc). Ideally you want this process done on the original mixed tapes or audio files, and not on top of an existing master.
There's also the process of producing a remix, where you grab the files produced in step 1 above and go through the process of remixing them. Mixing is the process where your whole soundscape is created, your stereo panning, individual instrument EQ, Reverb, Compression, etc. There's also the context of remixing in electronic music, where you grab existing tracks and rearrange them or implement them in different circumstances.