earldom vs domain

earldom and domain both are nouns.

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

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

Other hypernyms of earldom include demesne, land.

earldom (noun)	domain (noun)
the domain controlled by an earl or count or countess	the content of a particular field of knowledge
the dignity or rank or position of an earl or countess	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