secondary education vs teaching

secondary education and teaching both are nouns.

Word	Noun	Adjective	Verb	Adverb
secondary education	Yes	No	No	No
teaching	Yes	No	No	No

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

secondary education: education beyond the elementary grades; provided by a high school or college preparatory school
teaching: the activities of educating or instructing; activities that impart knowledge or skill

Other hypernyms of secondary education include didactics, education, educational activity, instruction, pedagogy.

secondary education (noun)	teaching (noun)
education beyond the elementary grades; provided by a high school or college preparatory school	the profession of a teacher
	the activities of educating or instructing; activities that impart knowledge or skill
	a doctrine that is taught