schooling vs training

schooling and training both are nouns.

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

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

schooling: the training of an animal (especially the training of a horse for dressage)
training: activity leading to skilled behavior

Other hypernyms of schooling include grooming, preparation.

schooling (noun)	training (noun)
the act of teaching at school	activity leading to skilled behavior
the training of an animal (especially the training of a horse for dressage)	the result of good upbringing (especially knowledge of correct social behavior)
the process of being formally educated at a school