Fires can be used for utility reasons, or even as a deliberate attack. Cities can potentially be claimed just by setting them on fire and leaving a fire resistant unit, like a red dwagon, inside the garrison. But this prevents the conqueror from razing the city for schmuckers.
All small fires are of this type. They are frequently used for utility reasons, like a camp fire, or as part of the fire special in battle. If left unattended, it is possible for one of these to become uncontrolled, but this is unlikely except as part of a deliberate enemy action. They can be put out by just about any type of unit.
A large and spreading fire is classified as uncontrolled. Uncontrolled fires can still be put out, but only if the side has uncontested control of the area. Any type of talking unit can potentially fight an uncontrolled fire. But some units, such as pink dwagons, firemen, and some water based units, can specifically engage fire instead of an enemy.
A huge fire is classified as an inferno. It causes heavy damage to units trapped inside. Dirtamancers are the only type of unit capable of putting out an inferno. If not extinguished, it will change the terrain type to ash and croak any unit without the fire resistance special that fails to evade trap at a penalty to flee area.