The question struck me as odd, but I suppose that you really need to know what you call your martial arts teacher. I have the kids call me coach, but it depends what martial art you are teaching. I don’t think anything is insulting, but here are some common teacher names for some common martial arts.
Japanese martial arts commonly use Sensei meaning “teacher” or literally translated, “born first” or “one who has gone before”.
A Sensei is a person who has knowledge and is willing to teach that knowledge to another.
Grandmaster (or Grand Master) and Master are titles used to describe or address some senior or experienced martial artists. Typically these titles are honorific in nature, meaning that they do not infer rank, but rather distinguish the individual as very highly revered in their school, system, or style. It is a badge of honor and respect that isn’t formal, but is a compliment.
Chinese Martial Arts like kung-fu usually call the teacher Sifu,, although the term and pronunciation are also used in other southern languages. In Mandarin Chinese, it is spelled “shifu”. Many martial arts studios pronounce the word like “she foo”. In Cantonese, it is said as “see foo” (almost like “sea food”, without the “d” on the end). The actual Korean word for a student’s master is suseung-nim. This term is only used by the student when speaking to the instructor. The student is hakseang. Many Korean titles are often mistakenly translated as “grandmaster”. The term is general term for any teacher of any subject as well as a respectful form of the word “you”. Coincidently, martial arts instructors (in Korea 4th Dan and above) are called Sabom-nim.
In the Muay Thai world, instructors are called Kru and Arjan. (also ajaan, ajarn, acharn, and achaan). These words do not by any means mean “Master.” Quite simply, they both mean “teacher.” They do not differ from society to the gym. Your english teacher or math teach would be referred to as Kru or Arjan. Although Ajarn is used for more experienced or respected teacher… it still translates the same as Kru. In the Muay Thai world, it is a tad disrespectful to call yourself a Kru or Arjan if you haven’t fought though. Although the term doesn’t mean that you are a fighter, it is commonly understood that the instructor was an actual fighter at some point.
The term that seems to have the most controversy is the name that BJJ practitioners call their instructor. Most of them just call them coach but others are referred to as Professors. I thought this to be a distinguished honor when I first heard it and it added some regal sense of mastery to anyone who was being called a Professor by their students. When I learned why, it was actually kind of underwhelming. The term is a literal translation from Portuguese (the national language of Brazil), that means simply: Teacher. So now you know what to call your instructors.