Great question Pat!
First of all, I want to clarify that limit orders could be either "buy limit" or "sell limit"; and stop orders could be either "buy stop" or "sell stop" orders. They are all classified as pending orders and they are placed in advance before price reaches them.
Limit orders can be executed at the price you specified or better, while stop orders can only be executed at the price you specified.
A buy limit order enables you secure a price below the current price so that when the price falls and reaches it, then it is triggered and you buy for cheaper. Even if the price gaps past it, it will still be executed at the next price.
A sell limit order enables you secure a price above the current price so it is activated when price rises and touches it. It also helps you sell for higher. Even if the price gaps past it, it will still be executed at the next price.
A buy stop order can only be placed at a price above the current price but it comes with a stop function/order such that if the price you set it at cannot be gotten, the order will be closed and not executed.
A sell stop can only be positioned below the current price and it also comes with a stop function/order so that if the price you set it at is unavailable, the order will be closed and not executed.
Personally, I do not use buy or sell stop orders because they are high risk and require going against healthy risk management rules of buying low and selling high.
I prefer to use limit orders because they encourage risk management of buying low and selling high, and they can be executed at a better price than I had specified.