Put a thermocouple in some hairdriers and you'll find some get well over 400 Celcius (750F!).
They just rely on the fact air has a low thermal mass, and it's easy to just keep it slightly further from your skin if necessary - the air quickly cools with distance as more room air mixes in.
There is a huge difference in whether one can actually reach that temperature, how quickly, and how much airflow it provides across the heating element and on target. A heat gun is a much more consistent tool for the uses for which it's designed.
A heat gun is also designed to put pretty consistent heat an inch or so away from the nozzle, whereas hair dryers often have what appear to be left-over jet engines for fans, for when you need to dry someone's hair from ten feet away.
They just rely on the fact air has a low thermal mass, and it's easy to just keep it slightly further from your skin if necessary - the air quickly cools with distance as more room air mixes in.