lesson vs teaching

lesson and teaching both are nouns.

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

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

Other hypernyms of lesson include instruction, pedagogy.

lesson (noun)	teaching (noun)
a task assigned for individual study	the profession of a teacher
a unit of instruction	the activities of educating or instructing; activities that impart knowledge or skill
punishment intended as a warning to others	a doctrine that is taught
the significance of a story or event