higher education vs pedagogy

higher education and pedagogy both are nouns.

Word	Noun	Adjective	Verb	Adverb
higher education	Yes	No	No	No
pedagogy	Yes	No	No	No

As nouns, pedagogy is a hypernym of higher education; that is, pedagogy is a word with a broader meaning than higher education:

higher education: education provided by a college or university
pedagogy: the activities of educating or instructing; activities that impart knowledge or skill

Other hypernyms of higher education include didactics, education, educational activity, instruction, teaching.

higher education (noun)	pedagogy (noun)
education provided by a college or university	the profession of a teacher
	the activities of educating or instructing; activities that impart knowledge or skill
	the principles and methods of instruction