why does my grill which has a thermometer on the top register one temperature, but I put a thermometer inside registers a different temperature, the difference is 100°F?
The thermometers built into the grill which is on the mounted to the top of the grill reads 100°F higher than a thermometer inside of the grill.
It's the first one. I can tell you for sure that there is a huge temperature gradient inside the grill from the distance from the cooking grates to the inside of the lid. The lid thermometer is somewhere between 10-14" away from the grates, in most models.
That's also why the upper rack is a "warming" rack and not a "cooking" rack (despite some manufacturers - coughweber - trying to include it in the cooking area total).
Most of the built-in thermostats on barbecue grills are garbage. Before speculating on what might be behind the temperature difference, get a thermometer that is accurate with two probes and measure again.
Thermometers, like most measurement devices, are always accurate until you get two of them. Each device has a specific tolerance (or should, otherwise it's probably a horrible tolerance), for a grill thermometer this will look like -/+5C/10F. Additionally, everything used to read a measurement needs to be calibrated regularly to ensure proper function, otherwise readings cannot be trusted. For a thermometer, the easily accessible way to calibrate are to use ice water (does it read 0C/32F) and boiling water (does it read 100C/212F). Using these constants will allow you to adjust your thermometer and get a (more) accurate reading.
Heat rises, cheapo thermometers aren't super accurate.
If you can get access to the probe itself, try the two easy extremes.... boiling water and ice water. See how far off they are. They will be off, it just depends by how much.
Of course the important metric when it comes to cooking food isn't the air temp, but the temp inside the food, which is why an internal thermometer is what most people go by.
I suspect it has something to do with how far away the thermometer is from the actual heat source. you can hold your hand over a flame and be relatively fine, but if you stick your hand directly into flame, you will be burnt.