arts vs bailiwick

arts and bailiwick both are nouns.

Word	Noun	Adjective	Verb	Adverb
arts	Yes	No	No	No
bailiwick	Yes	No	No	No

As nouns, bailiwick is a hypernym of arts; that is, bailiwick is a word with a broader meaning than arts:

arts: studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)
bailiwick: a branch of knowledge

Other hypernyms of arts include discipline, field, field of study, study, subject, subject area, subject field.

arts (noun)	bailiwick (noun)
studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)	a branch of knowledge
	the area over which a bailiff has jurisdiction