This is an issue of culture rather than vocabulary. It depends on the country and type of school concerned. 'Principal' is mostly used in the USA. 'Headmaster' is used more in Britain, although this does sound rather old-fashioned. These days we tend to prefer the gender-neutral term 'Head teacher' or simply 'Head'.

Yes. "Headmaster" is more traditional UK English, but we are starting to use "principal" more here too.

In case you were confused, "junior school" and "primary school" are the same, as are "senior school", "high school" and "secondary school".

My school consisted of a junior and a senior school. They were both one school, but the senior and junior schools were on two separate campuses across the road from each other. The entire school (senior and junior) was run by a headmaster, but the junior school also had a principal (who was in charge of the junior school, but was ultimately employed by the headmaster at the senior school). That's just my school though.

안녕하세요 :) Essentially, yes, but there are some differences depending on the country and school. Headmaster is more commonly used in British countries, instead of Principal. However, I've been told some schools can have a Headmaster AND a Principal. Principal is more commonly used in the USA, but at private or elite schools, the term Headmaster can be used instead.