When it comes to options, the names American-style and European-style have a lot less to do with geography than how they can be exercised. American-style options can be exercised at any time, for any reason, prior to expiration, up to and including expiration day. European-style options can be exercised only at expiration. The majority of index options that trade in the U.S. have European-style expirations.
One expiration type isn't necessarily better than the other, as they both have their advantages and disadvantages. As such, it's important for you to know which style of expiration your options have before you invest. Another interesting note, The Black-Scholes formula, one of the most famous ways for pricing options, uses European-style expiration in its model. While you're thinking about Black-Scholes, you might want to take the opportunity to learn more about the option Greeks, like delta and theta.