Each main subject will have a head of department in UK secondary schools. So at least Maths, English, History, Geography, Art and the Sciences. Their responsibilities are to: Provide leadership and focus, setting the tone, ethos and, through close liaison with the Deputy Head (Academic), ensure that the highest standards of teaching and learning are consistently delivered. They will be given a few hours a week to carry out these responsibilities, so will typically tach around 20 hours rather than 23. They are also get a bit more money for the role, which s known as a teaching and learning responsibility (TLR) payment.

The words used in the U.S. will probably not be the same in England or other English speaking countries. For example, we can't even agree upon what a "public" or "private" school means. Talking secondary education in the U.S. now, the person in charge of the academic side is the Principal. The people who run less academic departments (administration, building and grounds, finance, etc.) are called "superintendents" or "directors". They can also be called "officers", such as "chief financial officer".

In Australia in referring to schools, we would say "the department head" or "head of department", sometimes reduced to HOD. You would know which type of school and potentially the subject area, from the context of the conversation.

You might hear chairman/chairperson. I'm looking at a list of synonyms from ChatGPT, but I think really chairman/chairperson is the only one from that list that anyone might use in real life. You don't call the chairman of a department the "boss" or the "director" or the "manager", etc. However accurate those words might be, we don't use them in an academic setting, except "director", which in some regions the use for the headmaster/principal. The head/chairman of a department is responsible for a lot of boring administrative tasks. Once a chairman of a department told me his job was to sign things in triplicate. Usually if not always, they also teach. Aside from doing administrative tasks, I think in most schools a department chairperson is also the chief decision-maker about academic matters, such as the content of the curriculum. So for example the chairman of a math department is the chief academic officer within that department. Similarly, at a university there is always someone who holds a little like "provost", and he is the chief academic officer of the entire university. There would be one chairman for every major division of teaching: math, the sciences, language/literature, history, foreign languages, etc. I hope this helped. Cheers!