When you make these "tag" changes to fields such as Album Artist, Name, Track #, etc., you're making changes to the MC Library. This database (and some configuration settings) is what you'll Restore later. All your data and references to the external files will be available on some other system where you've installed MC, and Restored the Library.
You have:
- The MC Library
- Your media files (referenced by the Library)
Make both of these available on some other system in the future, and make any necessary changes to the Filename field (using the Rename, Move & Copy tool, in Update mode; for example, changing C:\Music to M:\Media\Music), and you've essentially completed the move. There are a couple of minor settings you'll perform on the new system.
Be clear, the Library does not contain the media files, and MC won't place these media files elsewhere. It only references the media you already have on some local or network file system.