ice rink vs ice-skating rink

ice rink and ice-skating rink both are nouns.

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

As nouns, ice rink and ice-skating rink are synonyms defined as:

ice rink and ice-skating rink: a rink with a floor of ice for ice hockey or ice skating

Other synonyms of ice rink include ice.

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