teaching vs school of thought

teaching and school of thought both are nouns.

Word	Noun	Adjective	Verb	Adverb
teaching	Yes	No	No	No
school of thought	Yes	No	No	No

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

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

Other hypernyms of teaching include doctrine, ism, philosophical system, philosophy.

teaching (noun)	school of thought (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