This. I did this with a math teacher (pre-calc and trig) I had at a community college years later when I was taking calculus etc in college and killing it (after having a less than stellar math education before and during highschool) and I think it was a huge deal to him. He really put his all into teaching that class and a lot of people probably went on to 4 yr college and didn't think much of it but after having professors that hardly spoke a word to their students and spent a straight hour just writing on a chalkboard I totally appreciated an invested, engaged math teacher.
The two aren't necessarily mutually exclusive. Sometimes just caring when no one else does can make someone a star... at least to the person they help.
I don't mean to denigrate the wonderful contribution that the teacher in question made, as it's truly a selfless commitment with life changing impact. However -
One distinction may be that the star teacher scales better. What if there were two students with this problem? Should the teacher stay late? Should teachers not take lunch? What if someone needs help in math, etc.
A star teacher may be able to reproduce this effect for a large number of students. Perhaps using technology, recorded lectures, practice apps, etc. Perhaps organizing study groups for kids to teach and learn from each other.
A caring teacher may sacrifice her lunch. A star teacher may not need to.
The thing about teaching is that you can be star just by having one success story. If you are a vital part of the success of 2 people you've already clearly contributed more than your share.
But one is enough; some of the most famous scientists only got where they were because they had a specific advisor. Neither the teacher nor student would ever have accomplished half as much working alone.
I am famous to maybe six people. So, it's not much. However, I wanted to add an account to this.
I can tell you the exact moment, problem, response, and teacher - that changed my life forever. It was at that single moment that I understood mathematics. I wasn't suddenly good at it. No, I still pretty much sucked at math. But, I understood it was a language and it was descriptive.
Many years later, that same teacher would be there to help me celebrate defending my dissertation. I didn't actually march, I was already to busy by the time spring rolled around. He's an old man, now. I still stop in and we are still fast friends.
That one comment changed my life. There's a not insignificant chance that it has had a small impact on your life, assuming you've been impacted by modern traffic engineering, or in some pedestrian venues, or had some goods delivered. All that from a single comment that is entirely obvious, in retrospect.
You might be a star programmer, but only if you re-wrote every single program exceptionally, because clearly it's not making a fundamental change to someone's life once that counts, you're not a star until you've done that for everyone ...?
Going above and beyond the expectations of your role in order to make a fundamental change to someone's life is enough to call someone a "star" IMO. It's not like someone asked you to personally pay them a bonus, you can award all exceptional effort s a "star" without problem.
I am not clear on what definition you are using for "star teacher". But it sounds like "caring" is in the set of things that are required to be a star teacher.
