As I wrote previously, a lot of it depends on the “point” that one is trying to make when he/she uses the terms “learning” and “working”.
For many (possibly most) people, the point they are trying to make is that they (or their husbands, etc.) are learning Torah all day. So if he has a job that involves learning they would call it learning regardless of the fact that he is paid. The issue for them is not the pay, but the learning.
So, for example, they would refer to someone who is a Rosh Kollel or someone who is a Rebbe in a Mesivta (high school) or Beis Medrash (post-high-school) as learning, since he is learning even though he gets paid for it. When you teach adult men, or older boys, you are learning. On the other hand, they might not refer to a second grade Rebbe as learning, since he is not learning even though he is teaching.
On the other hand, there are others who have a different point to make when they use the terms “learning” or “working”. For example, a girl who values learning but doesn’t feel that she would be able to support her husband in kollel might refer to someone who is a Rosh Kollel as “working” because her “point” is that she wants to marry someone who has a parnassah, so for her the difference between “learning” and “working” has to do with the paycheck.
Sometimes, the point is something different. Sometimes, people want to make a statistical point about the percentage of Chareidim who “work”. In that case, they would include anyone who teaches, since there is no reason not to count someone who teaches Limudei Kodesh as working, just like you would include someone who teaches limudei chol.
So like any other categorization, who gets included depends on the way you define your terms, and the way you define your terms depends on the reason why you are setting up these categories in the first place. I think this is also the reason why different people have different ways of categorizing terms like “Chareidi”,etc.
In any case, I think that a lot of people, if not most, use the first definition I gave.