In the old days it was just "ice", and it still means that also (technically "ís" in the context of ice cream is short for "rjómaís", or "cream ice"). But nowadays it's most commonly used just to mean ice cream; if you want a glass of ice, you need to ask for "klaki". Indeed, sometimes people jokingly refer to Iceland as "klakinn", or "the ice". "Ég er á klakanum" -> "I'm on the ice" - > "I'm in Iceland".
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As a reference, try doing a google image search for "ís":
https://www.google.is/search?q=%22%C3%ADs%22&biw=1920&bih=960&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjt4KK1pvDMAhXpLcAKHd3YDHYQ_AUIBigB
In the old days it was just "ice", and it still means that also (technically "ís" in the context of ice cream is short for "rjómaís", or "cream ice"). But nowadays it's most commonly used just to mean ice cream; if you want a glass of ice, you need to ask for "klaki". Indeed, sometimes people jokingly refer to Iceland as "klakinn", or "the ice". "Ég er á klakanum" -> "I'm on the ice" - > "I'm in Iceland".