When it is hot in Italy, you want to order a “caffe freddo” (cold coffee) which is sort of like a coffee milkshake. It’s a bit confusing because it is not a “frappe” which is a different drink. I include a photo here so that you can see that a frappe is a coffee which is frothed to the point where it has a frappe/froth/head on top. A caffe freddo has milk added, a frappe does not.
When you see the slush machines spinning with coffee colored caffe freddo, you know that summer has arrived. A caffe freddo is different from an iced coffee or milkshake.
As an aside, the milkshakes in Italy are quite liquid and not unlike a caffe freddo except that they are not always as cold. Also, you can get a milkshake most of the year but caffe freddo is a summer thing.