In our art we are referred to as instructors and not coach. I am however a coach at certain times. A coach is there for a specific purpose or competition which has a beginning and an end, it is only related to the sports aspect of our full martial art. If I am at a competition with students with the purpose of coaching or observing for selection for an international competition, I am in a coaching role. An instructor is much more than a coach, observing and guiding in a much larger capacity beyond a specific competition.
Many sport fighting styles or combat sports refer to their trainers as coach, rightly so, due to the fully sport nature of those styles. This tends to not be the custom in traditional martial arts.
Also in Taekwon-Do an instructor, especially a senior should be referred to as Sabum-Nim. Sabum translated as Instructor and Nim loosely translated as Sir or Mam. However one cannot call them selves 'Nim'. Therefore it is understandable why so many do not fully understand this.Here in SA, calling the instructor Sabum and not adding the Nim became common place for quite some time . I thank Grand Master Han Sam Soo one of the pioneers for his concise clarification on this. Taekwon