I presume its a wirelless thermapen.
In short, all measurements are flawed, and just an affront to the gods. You can just pick one, usually the digital one and never look back.
The longer answer is, dome temperature under-estimates the temp at the grate level (usually, if we are talking about indirect cooking), and is slow to measure a change in temperature.
Ambient sensors of meat stick probes have issues too. The heat shielding lets the probe respond slowly to temperature changes. The evaporative cooling around the meat also will read lower than the air temperature inside the grill.
The wired probe at the grate is the fastest to respond. It generally over-estimates the temperature due to the wire which will see some heat as well. And like I said, I found it can vary significantly depending on probe placement.
E: So the takeaway is there is no "true" cooker temperature. There are flawed measurements, and its more important to get consistent. Know when and why you cannot trust your probe, and adjust from there. Your 250F won't be my 250F.