teaching vs education

teaching and education both are nouns.

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

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

teaching: the profession of a teacher
education: the profession of teaching (especially at a school or college or university)

As nouns, teaching and education are synonyms defined as:

teaching and education: the activities of educating or instructing; activities that impart knowledge or skill

Other synonyms of teaching include didactics, educational activity, instruction, pedagogy.

teaching (noun)	education (noun)
the profession of a teacher	the activities of educating or instructing; activities that impart knowledge or skill
the activities of educating or instructing; activities that impart knowledge or skill	the profession of teaching (especially at a school or college or university)
a doctrine that is taught	the result of good upbringing (especially knowledge of correct social behavior)
	knowledge acquired by learning and instruction
	the gradual process of acquiring knowledge