ice-hockey rink vs ice

ice-hockey rink and ice both are nouns.

Word	Noun	Adjective	Verb	Adverb
ice-hockey rink	Yes	No	No	No
ice	Yes	No	Yes	No

As nouns, ice is a hypernym of ice-hockey rink; that is, ice is a word with a broader meaning than ice-hockey rink:

Other hypernyms of ice-hockey rink include ice-skating rink, ice rink.

ice-hockey rink (noun)	ice (noun)
an ice rink for playing ice hockey	a rink with a floor of ice for ice hockey or ice skating
	an amphetamine derivative (trade name Methedrine) used in the form of a crystalline hydrochloride; used as a stimulant to the nervous system and as an appetite suppressant
	a frozen dessert with fruit flavoring (especially one containing no milk)
	a flavored sugar topping used to coat and decorate cakes
	the frozen part of a body of water
	diamonds
	water frozen in the solid state