schooling vs teaching

schooling and teaching both are nouns.

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

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

Other hypernyms of schooling include instruction, pedagogy.

schooling (noun)	teaching (noun)
the act of teaching at school	the profession of a teacher
the training of an animal (especially the training of a horse for dressage)	the activities of educating or instructing; activities that impart knowledge or skill
the process of being formally educated at a school	a doctrine that is taught