With options markets, as with futures markets, long and short refer to the buying and selling of one or more contracts, but unlike futures markets, they do not refer to the direction of the trade. For example, if a futures trade is entered by buying a contract, the trade is a long trade, and the trader wants the price to go up, but with options, a trade can be entered by buying a Put contract, and is still a long trade, even though the trader wants the price to go down. The following chart may help explain this further:
American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.