Actually, if you call in a stop order, and the market is through your stop price when the order gets to the pit, it becomes a straight market order, not a market if touched order. If the market is at 798, and you put in a 800 buy stop, and the market is trading at 801 when it gets to the pit, it is elected and filled immediately. Some electronic systems will reject the order. If it became a MIT order, the market would have to trade back to 800 for it to get elected and then filled at the market.
The purpose of an MIT order, is if you want to buy a pullback or sell a rally to a certain price and be sure of a fill. Obviously if you use a limit order and it trades at your limit price, you are not necessarily going to get filled unless it goes through. The MIT will get you a fill if it goes to your price, turns on a dime, and goes back the other direction.
An easy way to keep the differences straight- With a stop order you are buying strength or selling weakness. With a MIT order, you are selling strength or buying weakness.