domain vs demesne

domain and demesne both are nouns.

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

As nouns, domain and demesne are synonyms defined as:

Other synonyms of domain include land.

domain (noun)	demesne (noun)
the content of a particular field of knowledge	territory over which rule or control is exercised
people in general; especially a distinctive group of people with some shared interest	extensive landed property (especially in the country) retained by the owner for his own use
(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