head teacher vs school principal

head teacher and school principal both are nouns.

Word	Noun	Adjective	Verb	Adverb
head teacher	Yes	No	No	No
school principal	Yes	No	No	No

As nouns, head teacher and school principal are synonyms defined as:

head teacher and school principal: the educator who has executive authority for a school

Other synonyms of head teacher include head, principal.

head teacher (noun)	school principal (noun)
the educator who has executive authority for a school	the educator who has executive authority for a school