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.
However, for put options (right to sell), the opposite is true - with strike prices below the current share price being considered "out of the money" and vice versa. And, what's more important - any "out of the money" options (whether call or put options) are worthless at expiration (so you really want to have an "in the money" option when trading on the stock market).
• Put Options – Give the buyer the right, but not the obligation, to sell the underlying at the stated strike price within a specific period of time. The seller of a put option is obligated to deliver a short position from the strike price (accept a long futures position) in the case that the buyer chooses to exercise the option. Keep in mind that delivering a short futures contract simply means being long from the strike price.