I think of it exactly as you say. IMO a “master” in MA is someone who’s mastered the art, relative to most others.
I think calling someone “master” has more implications of subservience to them rather than purely respect for them. It’s not completely rational on my part, and I recognize it. I just can’t bring myself to calling anyone that, ESPECIALLY when they demand it.
But “shihan” is the same term, just Japanese. And I have absolutely no qualms with that term. I don’t know the Korean, Chinese, etc terms, but I wouldn’t have problems with them either. Yeah, I’m weird. Fully admit it.
In the Chinese martial arts, we don’t tend to us such titles. Sifu means teacher, but it actually kind of means father, or someone who has gone before you, and it denotes a personal relationship between the two people. Sigung means grandfather, and it is your teacher’s teacher. Again, this is a specific relationship between the two people.
While someone could be Sigung to you, that same person would be Sifu to your teacher (your Sifu). So it is not a title to be worn. It is a word that describes a relationship.
There are additional terms to denote seniority in the school, terms that essentially mean brother or sister (as classmates) as well as elder and eldest brother and sister and younger brother and sister (I cannot remember the terms).
There is also uncle or aunt, who would be your sifu’s classmate.
One person could be each of these titles to different people, all at the same time. They could be Sigung to you, Sifu to your Sifu, brother to a classmate, younger brother to another classmate, uncle to his classmate’s student, etc., all at the same time.
There might be a term for Founder, I think it is Dai Sigung, but that means Great-Grandfather and is a bit more symbolic but it still denotes a relationship even if it is spanned over several generations. But other than that, not much for the actual titles like Master or Grandmaster.
It drives me a little nuts when I see people referring to themselves as Sigung, thinking it means Grandmaster. They want their own students to call them that. That is like me calling my own father, “Grandfather”. It just shows ignorance.