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This is a very basic question, that's ok but they often tend to get skipped over
A good way to learn about tags is to select any file and right click, and select Tag. On the left side of the screen a window will pop up with all of the tags, either empty or with the value that is in there currently. Browse through the tags and you'll get a handle on what's what....tags are what tells your PC what the files are....computers are smart but they can't listen to music or read liner notes!
For example on all your compilation records, assuming you have them in separate folders (and not just grouped into one single folder on the PC) you could browse by location, find one of those folders, select all the files, right click>tag, and type in (multiple artists) for the "album artist (auto)" tag. Now you have a single compilation album instead of 20 separate albums
For the other example (remaster disc), you could rename the album tag to say "II (remaster)", now it appears as a separate album from the original "II". Or, you could enter "remaster" into another tag field like "keywords", or you could change the date to reflect the remaster date. Those are all ways to differentiate between the original and the remaster. Grace note or CDDB likely won't have separate tag information so they can't be counted on to "know" the difference between the two
Tags are just information, and MC is the database that allows you to view and sort the information in any order you like. Remember though-if ANY tag is different (say one "album" tag has a different name then another, but the tracks are on the same album) then MC will think it's a different album, so your tags need to be accurate! And it's worth noting as well, that "tag" and "library field" are somewhat interchangeable terms. The "library field" is where you enter "tag data"