As I read your explanation, I get the sense that there are two places the tags live: a) inside my music file or b) to the MC database.
Correct. The contents of the MC database are what you see reflected in all of the views of your music in MC.
If this is correct, how are they related? Does MC import your music file, the derive from it a database of its own that it uses as tagging information?
I think you've got the right idea. When you have a brand new empty MC library, there's no data in the database. As soon as you import one or more files, MC reads the tags from the files and populates the database with their values for Artist, Album, song Name, etc.
You can edit these fields, and they are stored back in the database. Writing those same values back to the original music files is optional. There are some customers that never, ever, ever want MC to write values to their files.
The MC database can also store arbitrary fields that may not be supported by the music files themselves. For example you could import a bunch of WAV files, which have extremely limited tag support, and then edit lots of data about those files (Artist, Album, and lots more). MC knows that this data goes with these files. But it doesn't necessarily have to write it back to the files. MC only uses it's database to show you information about your files.
Which of the tagging fields controls the display of the Artist screen? That is, I have a number of albums of related music. i would like to collect them under one item in the Artist screen, since they are (more or less) from one Artist.
Tricky question. Let's start with this:
The Artist "screen" is a database view. You can look at what fields it uses and other details by doing Customize View on it. You can make your own views! You can edit existing views. Though most of the basic views are locked and will warn you that they are locked. You can change them anyway, but you'll get a warning before you do.
How to solve your "related artists" thing is kind of up to you. It might make sense to establish a new field, or fields, for related artists. Or it might make sense to set them all to the same [Artist] field value. You also might use the [Album Artist (auto)] field for this. It really depends on the specifics.
I have a small number of artists like this. For example:
D'Angelo
D'Angelo and the Village Vanguard
For these two "artists" which are practically the same thing, I have the [Artist] field set to appropriate Artist name above. Some are the first one. Some are the second one. But for ALL OF THEM, I have the [Album Artist (auto)] field set to "D'Angelo".
I just checked my Artists view and it is grouping by [Album Artist (auto)] so this does what I want it to. That might work for you. If you want to check yours, go to the artists view and then pull down the little arrow next to the word Artists and select "Customize view". Cancel out of it after you look around a bit.
I think that's probably enough information for now.
Best of luck to you.
Brian.