There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with "optionality" embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knock-out, knock-in, barrier options, lookback options, Asian options, and Bermudan options. Again, exotic options are typically for professional derivatives traders.
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:
However, options are not the same thing as stocks because they do not represent ownership in a company. And, although futures use contracts just like options do, options are considered lower risk due to the fact that you can withdraw (or walk away from) an options contract at any point. The price of the option (its premium) is thus a percentage of the underlying asset or security. 
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