Here are some of the types of Italian coffee drinks you can find. I’m not sure that these are the “only” ways to drink coffee, maybe there are Italian regions or individual bars that have invented their own kind of coffee beverage.
Caffè. If you ask for “un caffé” [oohn kahf-FEH]at the bar, you get what for us Italians is “the” coffee, i.e. a creamy and tasty quite strong espresso. Often, to avoid confusion with other kinds of coffee-based drinks, when you order just “un caffè”, the waiter may ask: “Normale?” [nohr-MAH-leh] i.e. normal? in which case the answer is: “Sì, grazie!” [See, GRAH-tsee-eh], meaning “Yes, thank you!”.
Caffè decaffeinato is a coffee deprived of caffeine. People normally drink it in the evening and after dinner to avoid the risk of staying awake during the night. When you order it, you can simply ask “un decaffeinato” [oohn deh-kahf-feh-ee-NAH-toh]o “un deca” [oohn DEH-kah].
Caffé doppio [kahf-FEH DOHP-pyoh] is simply a double dose of espresso.
Caffè ristretto [ree-STREHT-toh] is a very concentrated espresso, therefore it is small. It tastes very strong but its caffeine content is actually very low.
Caffè lungo [LOOHN-goh] is obtained by draining more water than usual and contains more caffeine than normal. When I went abroad and I asked for an espresso, I never found true espresso. What I had was rather what we Italians call a long coffee.
Caffè macchiato caldo [mahk-KYAH-toh KAHL-doh] is a normal espresso with addition of a little warm milk.
Caffè macchiato freddo [mahk-KYAH-toh FREHD-doh] is also a normal espresso in which you add cold milk with a small pot provided by the waiter.
Macchiatone [mahk-kyah-TOH-neh] is a long coffee prepared in a large cup with addition of frothed milk. It’s a cross between a macchiato and a cappuccino.
Caffè corretto [kohr-REHT-toh] is obtained by adding to a normal espresso a small amount of hard liquor. When ordering, you can specify what kind of liquor you want. In Veneto there is another version of this, the rasentin. You drink a normal espresso. When at the bottom of the cup remains only very little coffee, with the excuse to clean the cup, you add a little liquor (usually grappa), mix it to the coffee and drink.
Cappuccino [kahp-pooh-CHEE-noh] is a slightly long espresso with the addition of about 100 ml of frothed milk, served in a large cup, sometimes with a sprinkle of cocoa. In Italy we drink cappuccino almost exclusively at breakfast or during the morning, solo or accompanied by sweet foods. When foreigners order a cappuccino after lunch or accompanying it to savoury food, for us Italians it is a very strange thing, quite an abomination. I myself once, just once in my life, ordered a cappuccino and a sandwich at the same time. The waiter looked at me like I was crazy and have been teased by my friends for days. So be prepared!
Mocaccino [mok-kah-CHEE-noh] is a cappuccino with the addition of a little hot chocolate and cream, served in a transparent cup.
Marocchino [mah-rohk-KEE-noh] consists of milk foam, coffee and dark chocolate powder in a small transparent cup.
Caffellatte [kahf-feh-LAHT-teh] is an espresso mixed with about 200 ml of warm milk. Usually people drink it at home dipping biscuits in it during breakfast. It is similar to American latte.
Latte macchiato [LAHT-teh mahk-KYAH-toh] is warm milk served in a tall glass with the addition of an espresso poured on top.