You can get remixes, remasters, and a whole mess in between. It depends what your definition of "mastering" means as well.
A zillion years ago, the "master tape" was the final product of mixing. There was only one. From that one tape, copies were made that were send to the pressing plants to create acetate masters, then a "father", from which "mothers" were made, from which stampers are created and LPs were pressed. The creation of the pressing acetate master is itself a process during which the audio may be further processed. That processing of the master tape audio into a form best suited to the reproduction chain has since become known itself as "mastering." In the glory days of vinyl "mastering" as a separate process didn't really exist. Reproduction onto cassette tape was another chain, but the quality was worse than vinyl.
Enter digital, and for a time, a dual stream of reproduction was involved, and the audio mix suited to LP format was found to be wanting when it came to CD. Implicit knowledge used to make the result sound good on LP, taking into account its limitations sounded awful on CD. So we got "remastering" of the product. This was usually a matter of going to the master tape, and creating a reproduction "master" that suited digital.
Nowadays "mastering" is a separate step, usually done by a different engineer than the one responsible for the mixing, and takes the final mixdown, and applies frequency response tweaks and compression to the mix to create the final product for reproduction. Here is where the loudness wars were implemented.
In principle it is possible, at least for many recordings, to go back to the original mix, and create a new "mastering" that, for instance, does not have the worst horrors of the loudness wars. But it could go the other way. Someone might decide that a classic recording needs more pump and slam, and they wreck it. YMMV.
But we can go further back. Many recordings live on with their original tracking tapes in a vault somewhere. A 2inch multitrack behemoth, with all the original sound before mixing. There are a number of possibilities that may happen. The most interesting from a sound quality point of view is that we can extract better quality audio off the multitrack tape than was ever extracted before. The key is that we can digitise with enough bandwidth to see the bias signal on the tape. That gives us a known clock. Errors in tape speed can be corrected, and even better, scrape flutter can be corrected. As the tape runs past the heads it scrapes slightly, and this imposes a semi-random speed variation on the tape speed (flutter). This means the original recording had scrape flutter welded into it from day one. And subsequent replay just added more. But it is now possible to remove it. Careful analysis of tape formulations, head response and the like mean better sound than was ever heard since the moment of recording is available.
So you need to mix that down again. Neatly the big mixing desks usually had automation of the mixing levels, and the control signal may be available on the tape. So some recordings contain the most important aspects of the mixing too. But it is a remix. The remix may try to be as close to the original as possible, or someone might want to mess with it. But the potential exists for a new release of superlative quality.
Going back to the master tape and removing scrape flutter also helps, but you are still stuck with the previous generations so the result isn't as good as removing all scrape flutter.
Much depends on what sort of music you enjoy. Depeche Mode was one I never got into.
They have added new 5.1 DVDA tracks and outakes and alternative versions to every album.
