What is the difference between coffee and espresso?

Espresso is a type of coffee. More specifically, it's a method of brewing coffee that uses high water pressure and finely ground beans to make a small, concentrated shot. Espresso has a top layer of foam known as the crema, which is a by-product of the high-pressure extraction process.

When ordering a "coffee" in America, you will most likely get a drip coffee which is also a type of coffee. When you order un caffè (a coffee) in Italy, you will most likely receive an espresso.