This question of classifying combinations is, in fact, quite an interesting discussion.
<In classifying the combinations, I mainly consider which category will help me understand and master the tactic.>
This is of course the main thing, and, hence, as you also say, everybody should classify combinations in whatever way they feel help them do just that.
Having said that, however, I still feel that it does make sense to attempt an objective classification of combinations.
At worst, even if such a project didn't lead to an objective classification, it would lead to a thorough analysis of the subject matter, which cannot but help everybody achieve understanding and, therefore, mastery.
The problem with this particular combination is that there is a sense in which it is ONE threat - namely that is ONE move, Nb3, that is the problem.
But there is also a sense in which it is TWO threats - namely that the move has TWO different points.
So what is it? One threat or two threats?
That depends on how we ought to define a threat.
Is the threat to jump to b3 with the knight? Or is the threat to give checkmate?
In some sense both, but the latter must be the main content of a threat. We normally conceptualize a threat of eg scholar's mate as a threat of mate, not as a threat of moving our queen to f7. Of course it involves a movement of our queen, but it also involves a movement of our hand, but it seems that neither of these two movements are central to what is going on. The mate, on the other hand, IS central.
If the threat is 'to give checkmate' then there is also another threat - the threat of a royal fork.
And - as you say - two threats at the same time, according to the chess dictionary, is a double attack.
Therefore, I would classify this as a double attack, while adding that this is a special class of double attack where both threats are executed at the same square. This might sound odd, but is more common that most people realize. Another example of this tactic is the well known combination where the opponents king and queen are both on the back rank and we threaten to invade it with a rook. If he flees with the queen he is mated, if he makes luft he is forked/skewered/pinned, and, regardless, he is finished off with the same move of our rook to his back rank. This particular combination alone is quite common.
Of course someone might want to classify it as a case of 'bad king's position', and of course that would be correct, just as we might want to classify it as a combination that wins material, as a lot of different combinations do, and depending on what you want to achieve such a classification might be best, but I think such a classification is too broad to really UNDERSTAND what is happening. We need to penetrate into the heart of the tactic. Calling it a double attack with both threats on the same square, in my opinion, does just that.
And regarding your suggestion that since it wins the queen it might be classified as a case of a trapped queen, I must object that in that case virtually any combination that wins the queen should be classified as such.
To me, a trapped piece is a piece that is both threatened and dominated/obstructed, ie if it was a king it would be mate. This is clearly not the case here.
But - in the end - everybody has his own way of classifying combinations, and that's how it should be.