A call option is the right to buy a given asset at a fixed price on or before a specific date. A put option is the right to sell a given asset at a fixed price on or before a specific date. Calls increase in value when the price of the underlying asset goes up; puts increase in value when the price of the underlying asset goes down. A butterfly strategy is an options strategy using multiple puts and/or calls to make a bet on future volatility without having to guess in which direction the market will move.
A long butterfly strategy is constructed from three sets of either puts or calls having the same expiration date but different exercise prices (strikes). For example, with the underlying asset trading at 100, a long butterfly strategy can be built by buying puts (or calls) at 95 and 105, and selling (shorting) twice as many puts (or calls) at 100.
If the underlying does not change price by expiry, the puts at 95 and 100 will expire worthless, and the puts at 105 will be worth 5 (from 105-100). If the underlying is greater than 105 at expiration, all the puts expire worthless, and the initial cost of the butterfly is the amount of the loss. If the underlying is less than 95 at expiration, the gain from the purchased put at 105 will offset the losses from the shorted puts at 100, and the loss is again limited to the initial cost of initiating the butterfly strategy. In essence, this is a limited-risk, limited-gain approach to shorting the volatility of the underlying, as the maximum profit comes when the underlying has no volatility at all.
A short butterfly strategy is the converse; a limited-risk, limited-gain approach to being long (betting on an increase in) the volatility of the underlying. By buying the inside strike and selling the outside strikes, the position has its greatest loss when the underlying does not move, and its greatest gain when it moves beyond either of the outside exercise prices. A short butterfly strategy profits as equally from a large move up as it does from a large move down.
A regular butterfly strategy uses either all calls or all puts. A long iron butterfly sells a put and a call at the inside strike, and buys a put at the lowest strike and a call at the highest strike. A short iron butterfly buys a put and a call at the inside strike, and sells a put at the lowest strike and a call at the highest strike. In terms of profit and loss potentials, iron butterflies look very much like regular butterfly built from either all puts or all calls.
In general, the only time there is an advantage to choosing one type of butterfly strategy over another is if there is a pricing disparity in puts and calls making one of them cheaper to purchase or more profitable to sell.