Back testing is with a fixed spread that you set yourself whereas real life testing is with a spread set by your broker which can vary due to time of day  or current volatility. Slippage could also be the reason for the differences.

The missed stop loss might be due to minimum stop distances for the instrument that you are trading. I believe that if you send an order that is too close to price then it gets placed at whatever the current minimum stoploss distance is. I might be wrong on this and others might have more experience as I don’t use stop losses in my strategies.