country of origin vs mother country

country of origin and mother country both are nouns.

Word	Noun	Adjective	Verb	Adverb
country of origin	Yes	No	No	No
mother country	Yes	No	No	No

As nouns, country of origin and mother country are synonyms defined as:

Other synonyms of country of origin include fatherland, homeland, motherland, native land.

country of origin (noun)	mother country (noun)
the country where you were born	the country where you were born