1. an espresso
Ordering un caffè results in the delivery of a single-shot of espresso with a layer of froth on the top, served in a small cup.
The reason you drink it is not to quench your thirst, but to sip an intensely-flavored nectar that leaves behind a wonderful aftertaste.
2. a coffee
Most Italians do not have an espresso machine at home: they use a stovetop coffee pot called moka. In 1933 Alfonso Bialetti revolutionized home coffee-brewing in Italy with the introduction of the Moka Express aluminum stovetop brewer. This simple, reliable machine became a design icon of the 20th century and even today the Moka Express can be found in nearly 90% of Italian households. (Source: Bialetti website: company history)