A while ago, I wrote a post attempting to define the difference between a chiesa and a duomo. The post caught the eye of Italian student, Andrea Ferrario, that led to a wonderful dialogue on the challenges of the Italian language--and he agree, the interpretation of Italian churches is no exception! And, although tourist signs may point you to a "duomo," that may, in fact, not be what you are looking at. Read Andrea's wonderful and enlightening explanation (I might also point out that Andrea's English is far better than my Italian ever will be!):
The most common monuments you see in Italy are, of course, churches. But Italian language has many terms that means “church”, and so you can find that today you are going to visit a Duomo, tomorrow you'll see a Basilica and the day after a Cattedrale. What do all these words mean?
The proper term used for a Christian temple is chiesa, that translates directly to "church." So you can safely use chiesa to address any church (as in “bella chiesa!,” that means “nice church”). Cattedrale (Italian for “cathedral”) is the name given to the church in which the Bishop's chair (cattedra) is. Usually there is only one bishop in each city, and so there is only one cattedrale.
The Basilica was a Roman public building, a sort of tribunal. In the centuries after the Roman Empire, the term basilica started to mean “big church,” because the first big churches were built in the style of the old Roman basilicas. Some architectural elements that you can often find in a church (for example, columns, apses, naves) were already present in pre-Christian Roman buildings. Nowadays, most of the main churches in Italy have the formal name of Basilica followed by the name of a saint; for example, Basilica di San Pietro (in Rome), Basilica di San Marco (in Venice).
The word Duomo comes from the Latin domus, that means “house.” After the fall of the Roman Empire, Latin was spoken only by members of the clergy, and so domus started to be used to address the “house of God.” Usually the most important church in each city is called Duomo followed by the name of the city; for example, Duomo di Milano, Duomo di Monza. Often, the duomo of the city is also the cathedral church. As for every other church, the duomo is dedicated to a particular saint and this can lead to confusion when the alternate name (“Basilica di...”) is used. Note that it's slightly incorrect to call duomo a church if it's not actually called duomo; for example, there are no churches called duomo in Rome and asking a Roman “dov'è il duomo?” would attract confused looks.
So far, so good. The problem is that Italian people actually use the words cattedrale or basilica to mean “big church”, even if the one intended is not the cathedral church. If you are asking for directions to the main church, it would be better to say “dov'è la cattedrale?” rather than “dov'è la chiesa?,” because with the latter you could be directed to the local church and not to the one you want to see. Also, remember that sometimes the common name of the church is different from its true name; for example, the famous San Giovanni in Laterano (St. John Lateran) is actually dedicated to Christ Saviour, St. John the Baptist and St. John the Evangelist.