schoolmaster vs pedagogue

schoolmaster and pedagogue both are nouns.

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

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

Other hypernyms of schoolmaster include educator, pedagog, adult male, man.

schoolmaster (noun)	pedagogue (noun)
food fish of warm Caribbean and Atlantic waters	someone who educates young people
presiding officer of a school
any person (or institution) who acts as an educator