Hhhmmm!
I suspect the problem is going to be an inconsistency in one field (for example the composer field; that the detail on one track is slightly different to another track) or that the information you see is not from the field you thought it would be. (See below.)
I also suspect that when iTunes was originally designed no one thought too much about classical music and the complexities of its naming conventions. That's not a criticism - I think it's just one of those things. Imagine when iTunes and iPods were conceived; pop and rock music fans would design a player that suits them. How many of them are classical music fans as well? Subsequently however, iTunes and iPods have become so popular that classical music fans want in on them too and this has revealed a shortcoming of the original design. I say this as a pop and rock music fan who happens to like some classical music, but one who doesn't fully utilise the complexity of the naming system. I have however, seen many posts in these discussions from classical music fans who found that iTunes didn't have the facilities they want.
But this has changed with the introduction of the Work Name field. I confess that I have not used this up to now, but I've tested it in light of your post.

Looking at this piece, where I have just filled the Work and Movement fields, I noticed that even though I was copying from the Name field and pasting into the Work Name field, there is now a discrepancy:

Can you see it? The Song Name field omits the word Concerto, despite the fact that I copied from the Song and pasted into the Work Name. Up until my experiment for this discussion, I would have expected the Name field (2. shown below) and the Song (3. in the shot below) to be identical.

As you can see, they are not identical.
If I now look at the album in the Artists view, I see another strange thing:

First, notice the composer for Brandenburg #4 is バッハ, but in Get Info that is only for the first track. The following tracks use Bach, J.S. By now, you may well have spotted another problem: BWV 1050a. Allegro is part of Brandenburg Concerto #5, but here it is listed under Concerto #4. In Get Info it looks correct.

I can correct the composer name easily (and have done so), but I have yet to figure out why the piece from Concerto #5 is listed under Concerto #4. I'm working on it.
So how do you move forward?
Well, hopefully, someone else with in depth knowledge of classical music will contribute to this discussion and between you you may get somewhere. If one of those contributors has access to Apple's bug reporting, perhaps he or she will be able to submit a bug report and eventually the problem might get corrected.
None of my ageing iPods can handle the Work Name or Movement fields, which is probably why I haven't noticed this feature until now.
Finally, I copied the Song field from the piece above and pasted it into the Work Name field, so the only thing that changed was the removal of the word Concerto. But now, when I look in the Album view, Brandenburg #4 has gone too.

It's all above my intelligence level.