stopper vs bottle cork

stopper and bottle cork both are nouns.

Word	Noun	Adjective	Verb	Adverb
stopper	Yes	No	Yes	No
bottle cork	Yes	No	No	No

As nouns, bottle cork is a hyponym of stopper; that is, bottle cork is a word with a more specific, narrower meaning than stopper:

stopper (noun)	bottle cork (noun)
blockage consisting of an object designed to fill a hole tightly	the plug in the mouth of a bottle (especially a wine bottle)
(bridge) a playing card with a value sufficiently high to insure taking a trick in a particular suit
an act so striking or impressive that the show must be delayed until the audience quiets down
a remark to which there is no polite conversational reply

stopper (verb)	bottle cork (verb)
close or secure with or as if with a stopper