teaching vs philosophy

teaching and philosophy both are nouns.

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

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

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

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

teaching (noun)	philosophy (noun)
the profession of a teacher	the rational investigation of questions about existence and knowledge and ethics
the activities of educating or instructing; activities that impart knowledge or skill	a belief (or system of beliefs) accepted as authoritative by some group or school
a doctrine that is taught	any personal belief about how to live or how to deal with a situation