Quick transactions refer to a transaction where the user inputs the receiving address and is given a deposit address from ShapeShift. With this quick order, the user does not need to tell us how much of a certain altcoin they want to receive and they can deposit whatever they would like, as long as it is between the deposit limit (max) or minimum.
Precise transactions (also know as specific amount orders) refer to a transaction where the user tell ShapeShift how much they are wanting to deposit BEFORE we provide you with a deposit address. We tell you how much of the receiving coin you would receive with that amount deposited and then supply you with an address to deposit that precise amount you specified to us you would like to deposit. You can get a better rate with this type of order AND a higher deposit max.