ice vs ice hockey rink

ice and ice hockey rink both are nouns.

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

As nouns, ice hockey rink is a hyponym of ice; that is, ice hockey rink is a word with a more specific, narrower meaning than ice:

Other hyponyms of ice include ice-hockey rink.

ice (noun)	ice hockey rink (noun)
a rink with a floor of ice for ice hockey or ice skating	an ice rink for playing ice hockey
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