church vs cathedral

church and cathedral both are nouns.

Word	Noun	Adjective	Verb	Adverb
church	Yes	No	Yes	No
cathedral	Yes	Yes	No	No

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

Other hyponyms of church include abbey, basilica, duomo, kirk.

church (noun)	cathedral (noun)
a service conducted in a house of worship	any large and important church
a place for public (especially Christian) worship	the principal Christian church building of a bishop's diocese
one of the groups of Christians who have their own beliefs and forms of worship
the body of people who attend or belong to a particular local church

church (adjective)	cathedral (adjective)
	relating to or containing or issuing from a bishop's office or throne

church (verb)	cathedral (verb)
perform a special church rite or service for