Both meanings are very similar in the dictionary, but 发火 also means to 'get angry' and 'to detonate'. Can they be used interchangeably and what is the difference between the two words?
发火 is usually used metaphorically for a person, meaning getting angry. For example, you can say to someone 别发火/don't get angry, 他又发火了/he is angry again.
着火 is usually used as its literal meaning for a real object. Xxx 着火 means xxx catching fire/be on fire. For example, 房子着火了/ the house caught fire.
Basically, they won't be used interchangeably. We don't say 他又着火了 or 房子发火了.