A little difference :) imagine someone can be very 生气, but hold it back in so no one can see. But, 发火 is like a volcano eruption and you let everything out! Hope it helps. :)

生气Means you're angry. 发火Means You show your anger.

发火是生气之后更加严重的生气。

The former is more applied in the writing and the latter is in the causal chat!