ice rink vs skating rink

ice rink and skating rink both are nouns.

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

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

ice rink: a rink with a floor of ice for ice hockey or ice skating
skating rink: building that contains a surface for ice skating or roller skating

Other hypernyms of ice rink include rink.

ice rink (noun)	skating 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