teaching vs doctrine

teaching and doctrine both are nouns.

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

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

teaching: a doctrine that is taught
doctrine: a belief (or system of beliefs) accepted as authoritative by some group or school

Other hypernyms of teaching include ism, philosophical system, philosophy, school of thought.

teaching (noun)	doctrine (noun)
the profession of a teacher	a belief (or system of beliefs) accepted as authoritative by some group or school
the activities of educating or instructing; activities that impart knowledge or skill
a doctrine that is taught