Is Italian ice in Italy just called ice?

The closest thing to Italian ice in Italy is actually granita.

It is a semi-frozen dessert made from sugar, water and (usually) fruit-based flavorings. It originates in Sicily, but can be found all over Italy.

In Rome, street vendors also sell shaved ice flavored with various colorful syrups, which is a similar refreshing treat, and is called grattachecca.

When the temperature surges over the summer, stands and kiosks that are in the grattachecca trade make good money.