public school vs United Kingdom of Great Britain and Northern Ireland

public school and United Kingdom of Great Britain and Northern Ireland both are nouns.

Word	Noun	Adjective	Verb	Adverb
public school	Yes	No	No	No
United Kingdom of Great Britain and Northern Ireland	Yes	No	No	No

public school (noun)	United Kingdom of Great Britain and Northern Ireland (noun)
a tuition free school in the United States supported by taxes and controlled by a school board	a monarchy in northwestern Europe occupying most of the British Isles; divided into England and Scotland and Wales and Northern Ireland; `Great Britain' is often used loosely to refer to the United Kingdom
private independent secondary school in Great Britain supported by endowment and tuition