The best way to think of it is that the stop-limit is a series of orders.
The stop price is an order where once the trading price of AAPL passes your "stop price" of $323.60, the stop order says "go"
Your limit order says that you will buy 50 shares of AAPL at $323.60 per share or lower. That is how limit orders work. Once your stop order says "go" your limit order hears this command and becomes active:
That's why it's called a "stop-limit"
So at this point you have a stop-limit order out to buy 50 shares of AAPL at $323.60 or better. If the price passes $323.60 (your stop) and then activates your limit order, (at $323.60) but then continues to rise to $325 without ever coming back down to $323.60, then your limit order will never be filled.
This is why traders often like to set their stop price different than their limit price.
You might set the stop price at $323.60, but then set your limit to $324. That way if $323.60 is passed, you will hopefully pick up the shares at $324 or better before the stock runs up to $325 and beyond.
Traders often prefer stop-limits over "stop" orders because if you have a stop order with no limit, your stop activates a market order where you are willing to pay whatever the market price is for 50 shares.
If some important piece of news comes out, like say AAPL sues Microsoft and wins $50 billion, the stock might skyrocket to $500 in an instant. If you have a stop-market at $323.60, your stop would be triggered and you would have an order to buy 50 shares of AAPL at $500, which you may or may not actually be able to afford. That's the danger to a stop-market.
Rule of thumb, ALWAYS use limit orders, whether you are using a stop or not.