Fires are much more dangerous in space. Spaceships are enclosed systems, you can't just vent the heat and toxic smoke the way you can on Earth. On the other hand, ships will be designed presuming that you need to close down entire sections of the ship at a time from air flow, either because of a hull breach or because of a fire or any other disaster, so fire control is a lot easier; just let the fire consume all oxygen and if possible use the cooling system to chill the local temperature to below the ignition temperature. Or, for that matter, open the burning sections to hard vacuum, it'll resolve itself soon enough.