academe vs domain

academe and domain both are nouns.

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

As nouns, domain is a hypernym of academe; that is, domain is a word with a broader meaning than academe:

academe: the academic world
domain: people in general; especially a distinctive group of people with some shared interest

Other hypernyms of academe include world.

academe (noun)	domain (noun)
the academic world	the content of a particular field of knowledge
	people in general; especially a distinctive group of people with some shared interest
	(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