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).