school principal vs head teacher

school principal and head teacher both are nouns.

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

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

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

Other synonyms of school principal include head, principal.

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