domain vs archduchy

domain and archduchy both are nouns.

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

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

domain (noun)	archduchy (noun)
the content of a particular field of knowledge	the domain controlled by an archduke or archduchess
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