The Paladins in Perilous Paths emerge from the monastic traditions of the Holy Church, and their vows of poverty, humility, and obedience. Paladins (the important ones anyway) are also known as Justicars, and their most important function in society is to deliver Justice.
The Red Paladins of Mithras and the Blue Paladins of Venus do have significantly differing views on what Justice looks like (Red Paladins look more like the Inquisition, Blue Paladins practice restorative justice more akin to the Salvation Army). Still, both are wiz-bang terrifying combatants in the field. Owing to that poverty vow, neither practice extensively in armor (a big difference from D&D / Dungeon World default Paladins).
Red Paladins are more like Kensai Sword-Saints. The most expensive item in their possession will be a longsword, and the longsword belongs to the church. And they do Fighter damage with those.
Blue Paladins are more like (far-eastern) fighting monks. The most expensive item in their possession is a quarterstaff, which belongs to the paladin. They do Fighter damage with the staff, and with their bare hands. (Which is technically true for Red Paladins and Fighters, but as a narrative truth, Blue Paladins have kung-fu, which is A Big Deal).
The backstory is that Red Paladins learned their martial traditions from the fire Djinn, and the Blue Paladins learned their traditions from wind Djinn.