What is the difference between extra fire or burning damage, when using Righteous Fire?

This page on PoE Wikipedia says

The burning damage over time is 40% of the base damage of the hit of fire damage, per second

Righteous Fire does not hit, but its burning damage per second is still increased by 40% of the base fire damage a character would deal. Therefore both modifiers have the same effect.

I tried this with Demi's RF Build using Path of Building . I removed all Jewels he used, resulting in 402887.5 DoT DPS. Adding a Jewel with 16% increased Burning Damage resulted in calculated DoT DPS of 411467.1 . Adding a 16% increased Fire Damage Jewel instead resulted also in 411467.1 DoT DPS.