schooling vs education

schooling and education both are nouns.

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

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

schooling (noun)	education (noun)
the act of teaching at school	the activities of educating or instructing; activities that impart knowledge or skill
the training of an animal (especially the training of a horse for dressage)	the profession of teaching (especially at a school or college or university)
the process of being formally educated at a school	the result of good upbringing (especially knowledge of correct social behavior)
	knowledge acquired by learning and instruction
	the gradual process of acquiring knowledge