What is the difference between principal and headmaster?

They are the same thing: the head of a school. The terms are used differently in different countries, and sometimes even interchangably.

In the U.S., a "principal" tends to be the chief administrator of a public (that is, state-supported) school, while a "headmaster" or "headmistress" has the same function at a private school. There are exceptions to this, though.

American private schools borrowed the term "headmaster" from British models for elite fee-paying schools, in which a "headmaster" is sometimes a school's senior teacher.

"Principal" or "Head of School" is often used as the title of the head administrator of an elementary school, middle school, or high school or boarding school in some English-speaking countries, including the United States, India, Australia and New Zealand. Public schools in the United States generally use the title "principal" whereas private schools in the United States sometimes use the title Head of School.

https://en.wikipedia.org/wiki/Head_teacher

In England and Wales the terms "Headmaster" and "Headmistress" used to be standard at most schools (whether in the private or public sector). More recently, the term "Head" has become widespread as a non-sexist designation. "Principal" is used at a few schcools, but it tends to be associated with sixth-form colleges and colleges of further education.

In Scotland the term "Principal" is, I think, more widely used than in England, and the impressive sounding title "Rector" is also used at some schools in Scotland. However, it should be taken with as large a pinch of salt as the Scottish use of the title "Academy" in the names of some secondary schools.

I was brainwashed in the fifth grade and for spelling we were told that the headmaster was the master of our head and the principal was our pal. Probably why I spent so much time in his office.

Bloomsby, "Head" has become fairly common here, too -- the girls' school I attended is now administered by a "Head" -- and I know of at least one private U.S. boarding school, affiliated with the Episcopal Church, in which the chief executive is called "the Rector."

Many thanks, Frankie. In England, a few schools have a "High Master", but I haven't yet heard of a "High Mistress".

Abbrevations, too, can be fun, such as HM. The few schools where the Deputy Headmaster or Headmistress is called the Second Master or Mistress aren't too keen these days on the abbreviation SM for the post. :)

I went to US private Catholic school for all my years of study and the term "principal" was used.

However, I think "headmaster" would be more common in a very elite private boarding or day school.

Principals and Headmasters/mistresses are the same things. They have the same job but in different countries their called different things, like in the UK its headmaster and in the US its principal.