The grill is closer to the fire, so the measured temperature is also higher. A difference of, say, 35 degrees Celsius is certainly not crazy. As a result, your dome thermometer may indicate a different temperature than a thermometer close to the rack in the dish.
Tip; want to achieve a high temperature for e.g. baking pizza? Then keep in mind that when your dome thermometer shows the desired temperature, the pizza stone has already reached a much higher temperature. So take this into account in determining the ideal temperature.
So what is the ideal temperature for baking a pizza? There is no single answer for that, everyone has their own preferences.