Below I have listed some of the terms and distinctions to help you decipher the myriad of terms Italians use to describe their gustatory havens. Of course these are generalizations: a ristorante in a town off the beaten path may be cheaper and less swanky than a trattoria in the city center. And many establishments attempt to capture all the price points and offer a ristorante, caffe, and enoteca on the premises!
Ristorante: Formal restaurant, generally the most expensive. Expect to need reservations and to dress nicely.
Trattoria: Usually cheaper and more casual than a ristorante. Often it is a local hang-out, with the menu written in chalk on a board, rather than printed and handed to you.
Osteria: The word means hostel/inn, but usually they just serve food, in the same vein as a trattoria.
Caffe: Many eating places have Caffe in their name, but are more like a trattoria in the wide selection of food available. The one constant is that you can be pretty sure that they will be open for breakfast and happy to serve you a cappuccino and brioche.
Pizzeria: Not surprisingly, a place that specializes in pizzas, though they often provide a selection of pastas and secondi. Unlike American restaurants, you order one pizza per person, and it will be about 10-12 inches wide. Fear not, it will have a very thin crust. You can eat it in one sitting, but don't expect to eat dessert afterwards. Shops sell Pizza al taglio by the slice (actually by weight) to-go, with a thicker crust.
Bar: This one surprises Americans. Bars (sometimes called caffe-bars) serve everything from coffee to food, like ice-cream treats and pannini. No over-21 signs here either, and kids pop in to buy candy. Yes they do serve alcohol, too. Of course, a decent glass of wine may be cheaper than una Coca Cola. Ironically, many of these multi-purpose establishments bill themselves as "un Bar American."
Pub/ Birreria: What Americans think of as a bar: drinks and sparse food. Disco-Pubs are the Italian equivalent to clubs- open later with music and more expensive drinks.
Enoteca: A wine bar where you sample different varietals by the glass. At some food may be offered, but it is secondary to the wine. Others are more like wine shops that may or may not serve by the glass. Don’t ask for beer here.
Tavola Calde: To-go food (literally hot tables). Generally McDonald's and its European cousins fall here, but some of these places, especially the ethnic ones, serve decent fare. Similar quality food is available in cafeteria and un "self-serve", which offer the additional amenity of seating to eat your repast.
This is only a subset of terms, there are also rosticceria (places selling roasted meats, either to-go or with service onsite), alimentari or mercati are grocery shops where you can buy picnic supplies. A panicoteca makes hot or cold sandwiches to order for you. And you can satisfy your cravings for baked goods or ice cream at a pasticceria or a gelateria.