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).
In, At, or Out of the Money: If an option is in the money, its premium will have additional value because the option is already in profit, and the profit will be immediately available to the buyer of the option. If an option is at the money, or out of the money, its premium will not have any additional value because the options are not yet in profit.