先生 is a title, like Sir, Mr, Mrs, Dr, etc, and it means Professor, or Pro. It is added to the name:
鈴木さん (Mr. Suzuki);鈴木先生。(Pro. Suzuki)
It is the title for teachers and professors of all branches, including masters of martial arts. Being a title, you NEVER use it to refer to yourself! Just like you never call yourself Sir, or Madame. You cannot call yourself "san", "sama", or "sensei".
教師 = teacher or professor. When someone asks you what you do you say: 教師です。 You never say 先生です。