ice vs rink

ice and rink both are nouns.

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

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

Other hypernyms of ice include skating rink.

ice (noun)	rink (noun)
a rink with a floor of ice for ice hockey or ice skating	building that contains a surface for ice skating or roller 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