Charlie will have an excellent answer, but pardon me if I barge in. YES, there are different grades
of espresso, just as there are different grades of "regular" drip coffee. Espresso is also a degree of roasting, not just a grind. Espresso is the darkest roast, giving it a distinctive flavor. Because the brewing method takes only about 30 seconds, with sometimes even less contact between the water and the coffee grounds, you'd want to use the appropriately roasted beans. If you use your regular coffee, you'll probably end up with a weak, acidic brew, no matter how fine the grind.
A good brand of espresso, such as Lavazza, is made only with Arabica beans. Lesser (though perfectly acceptable to many people) brands start with Arabica but add less-complex robusta beans, sometimes double-roasting them for boosted flavor.