head teacher vs pedagogue

head teacher and pedagogue both are nouns.

Word	Noun	Adjective	Verb	Adverb
head teacher	Yes	No	No	No
pedagogue	Yes	No	No	No

As nouns, pedagogue is a hypernym of head teacher; that is, pedagogue is a word with a broader meaning than head teacher:

Other hypernyms of head teacher include educator, pedagog.

head teacher (noun)	pedagogue (noun)
the educator who has executive authority for a school	someone who educates young people