EuroCity (EC) trains only operate across international borders. Those are similar to Italy's InterCity trains, but while InterCity trains only operate within Italy, EuroCity trains connect city to city at international level.
All EC trains must meet a certain level of service, including air conditioning in all cars and a dining car on every train. There are first and second class cars, and some amenities are only available in first class (such as power outlets at each seat). Speeds on EC trains vary, but they must all travel at least 56 MPH (90 km/h), except in special circumstances when the landscape demands slower speeds for safety.
EuroCity trains connect cities all over Europe, including Milan and Venice.