metropolitan vs archbishop

metropolitan and archbishop both are nouns.

Word	Noun	Adjective	Verb	Adverb
metropolitan	Yes	Yes	No	No
archbishop	Yes	No	No	No

As nouns, archbishop is a hypernym of metropolitan; that is, archbishop is a word with a broader meaning than metropolitan:

metropolitan: in the Eastern Orthodox Church this title is given to a position between bishop and patriarch; equivalent to archbishop in western Christianity
archbishop: a bishop of highest rank

metropolitan (noun)	archbishop (noun)
a person who lives in a metropolis	a bishop of highest rank
in the Eastern Orthodox Church this title is given to a position between bishop and patriarch; equivalent to archbishop in western Christianity

metropolitan (adjective)	archbishop (adjective)
relating to or characteristic of a metropolis