bottle cork vs stopper

bottle cork and stopper both are nouns.

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

As nouns, stopper is a hypernym of bottle cork; that is, stopper is a word with a broader meaning than bottle cork:

Other hypernyms of bottle cork include plug, stopple.

bottle cork (noun)	stopper (noun)
the plug in the mouth of a bottle (especially a wine bottle)	blockage consisting of an object designed to fill a hole tightly
	(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

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