teaching vs lesson

teaching and lesson both are nouns.

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

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

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