The difference between a firefighter and a smoke diver is that a firefighter aims to extinguish the fire or at least limit the damage caused by the fire and save people and animals from burning, while a smoke diver saves people (including firefighters) from the danger of smoke inhalation and limited oxygen supply resulting from the fire (which hogs a lot of oxygen). The skills learned and applied by the smoke diver include the use of specialized equipment. The link below will explain some more:

https://www.fsi.illinois.edu/content/courses/programs/descri...

Incidentally, smoke divers are not called smoke divers everywhere. Different cities use different terms, so there is no need to adhere to the words "smoke diver" when you translate.