domain vs bailiwick

domain and bailiwick both are nouns.

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

As nouns, bailiwick is a hyponym of domain; that is, bailiwick is a word with a more specific, narrower meaning than domain:

domain (noun)	bailiwick (noun)
the content of a particular field of knowledge	a branch of knowledge
people in general; especially a distinctive group of people with some shared interest	the area over which a bailiff has jurisdiction
(mathematics) the set of values of the independent variable for which a function is defined
territory over which rule or control is exercised
a particular environment or walk of life