"Hair dryer" is such an imprecise term in a use case like this. One can find 600 watt units all the way through about 2300 watts. A typical general-purpose heat gun one might use to strip paint or shrink some heat-shrink plastic is usually between 1500 watts and 1800 watts.

While the power consumption may vary considerably, the maximum temperature is presumably constrained by what humans and their hair can tolerate.

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.