county town vs shire town

county town and shire town both are nouns.

Word	Noun	Adjective	Verb	Adverb
county town	Yes	No	No	No
shire town	Yes	No	No	No

As nouns, county town and shire town are synonyms defined as:

county town and shire town: the town or city that is the seat of government for a county

county town (noun)	shire town (noun)
the town or city that is the seat of government for a county	the town or city that is the seat of government for a county