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In India in most schools, a female headmaster of a school is always referred to as "headmistress". Also "master" for teacher is almost always used; so "English master", "English mistress", etc. Female teachers are refered to as "mistress", or more commonly "miss".
I think much of this information is wrong
Public school, grammar school, and comprehensive school usage
I dispute the claim that 'Headmasters' exist only in public schools and, colloquially, in grammar schools. Not so many years ago I attended a comprehensive school which emphatically had a Headmaster, Deputy Headmasters, and Senior Master. These were the titles which these men used on their writing paper. It was absolutely official that they were designated types of master and not types of teacher. Most of the other teaching staff were indeed known as teachers, although there were several older masters who described themselves and their colleagues as 'masters'. Further, I know from young adults who were recently educated at public schools and from personal experience of public schools that the word 'master' is increasingly going out of fashion in those establishments as well.
I suspect that the hierarchy of masters was written with reference to one particular institution. At my own school we had a Headmaster, two Deputy Headmasters, and a Senior Master, who ranked beneath the Deputy Headmasters. In some schools the Senior Master may indeed be the headmaster's deputy, but there are many schools in which he ranks below the deputy headmaster(s) and is mostly responsible for discipline. The Senior Master at my school kept a couple of canes propped up in the corner of his study many years after he had ceased to be able to use them. The school was sufficiently modern that our teachers didn't wear gowns in the classroom, but the headmaster, deputy headmasters, and senior master unfailingly wore them to hold assemblies. I also dispute that the Second Master ranks third. There are certainly schools I know of where the Second Master is precisely that - the second master, ranking immediately after the Headmaster.
Other particular terms
The article does mention that other terms are also used. Most importantly, there are a number of schools where the headmaster is simply 'The Master', as in certain Oxbridge colleges. I think there is a sense in which all headmasters are 'The Master' because there is a slightly pedantic term for schoolmasters, which is 'Assistant Master'. I once worked for a rather old-fashioned institution which had dealings with the teaching profession, where that was the accepted term. It was so pedantic that one 'Assistant Mistress' wrote to complain that she was neither a mistress nor an assistant, but it had to be explained to her that as far as we were concerned she was an assistant mistress because she assisted the one true Master or Mistress of her institution. It was rather like the Emperor being proconsul of the imperial provinces.