teacher vs pedagogue

teacher and pedagogue both are nouns.

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

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

Other hypernyms of teacher include educator, pedagog.

teacher (noun)	pedagogue (noun)
a personified abstraction that teaches	someone who educates young people
a person whose occupation is teaching