education vs teaching

education and teaching both are nouns.

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

As nouns, education and teaching are synonyms defined as:

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

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

As nouns, teaching is a hyponym of education; that is, teaching is a word with a more specific, narrower meaning than education:

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

Other hyponyms of education include instruction, pedagogy.

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