Righteous Fire has the effects
Enemies Burn for 40% of your maximum Life per second as Fire Damage
Enemies Burn for 40% of your maximum Energy Shield per second as Fire Damage
indicating that the damage it inflicts is a "burning" one.
What is the difference between using a jewel with "increased fire damage" instead of one with "increased burning damage"? Which one has a large effect on the damage I deal?