course of study vs teaching

course of study and teaching both are nouns.

Word	Noun	Adjective	Verb	Adverb
course of study	Yes	No	No	No
teaching	Yes	No	No	No

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

course of study: education imparted in a series of lessons or meetings
teaching: the activities of educating or instructing; activities that impart knowledge or skill

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

course of study (noun)	teaching (noun)
education imparted in a series of lessons or meetings	the profession of a teacher
an integrated course of academic studies	the activities of educating or instructing; activities that impart knowledge or skill
	a doctrine that is taught