political arena vs domain

political arena and domain both are nouns.

Word	Noun	Adjective	Verb	Adverb
political arena	Yes	No	No	No
domain	Yes	No	No	No

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

Other hypernyms of political arena include area, arena, field, orbit, sphere.

political arena (noun)	domain (noun)
a sphere of intense political activity	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