Religion describes everything religious about a religion, including beliefs, building styles, clerical clothing, iconography, traditions, and so forth. Whether one believes in religion is irrelevant. One doesn't need to believe in Santa in order to wear a Santa suit.
Faith refers to beliefs, especially the beliefs of an individual or group. Both Anglicans and Catholics are arguably part of the same religion, the Christian Church. Outwardly they look very similar, but their faiths, the particulars of their belief, differ greatly. Faith, the adherence to belief, or the depth of that belief, matter a great deal in the Christian world.
In the pagan world, before monotheism and Christianity, faith wasn't really a thing. How sincerely you believed didn't matter. You were not assumed to have a personal relationship with a god. Worship belongs more at the community or family level, where groups established relationships with the divine. The maintenance of ritual mattered more than your own feelings or convictions. You don't have to like your superiors in order to make nice to them.
People were also free to engage in religion at whatever level that they pleased. They could add or subtract various aspects of their culture's religion because there were so many pieces, nobody did them all. Some people may sacrifice often while others never bothered. Some people joined many mystery religions, seeking more than the dominant religion could offer, while others only bothered with the feast days. Others didn't believe in gods at all, finding the whole idea of literal gods silly. In this way, religions more resembled a smorgasbord than a complete package, an approach that we see more of today in the West.
Paganism freely contradicts itself, and that's not a problem. The continuity editing was atrocious but nobody cared. The temple in one city believed one thing, with one set of stories, and a temple over in another city believed a different thing, with a different set of stories, and they both accepted each other in their worship of the same god. Differing beliefs were assumed because you came from different places.
The only thing that really mattered with paganism was not screwing up the community's relationship to the gods. If you went around doing blasphemous things, the gods wouldn't just blame you, they'd blame everybody, so the community had to shut down any stupidity fast.
In the world of hunter-gatherers and tuber culture, faith doesn't matter. Religion isn't distinct from culture in any meaningful sense. Religion, culture, history, law, and wisdom are simply not differentiated for those people. Faith in that context makes even less sense, because for those people, what is is. What is is obvious. There's no need for faith.
The question of faith itself is fundamental to Monotheism. In a pagan world, where you worship everything, your individual belief or non-belief in a god didn't matter. In a monotheistic world, where there is only one divine, and he knows what you're doing, the relationship between god and humanity changed radically. A personal relationship with God was now directly affected by your belief, or lack of it.
Monotheistic religion also came in a more tightly integrated package. You didn't get to add and subtract with equal enthusiasm (but that didn't keep early Christians from trying). The contents of the religion were more regulated, which resulted in more people splitting off from the main body and forming their own congregations. Because keeping a widespread religion believing the same thing was much harder, figuring out who believes what became a big deal. Monotheism spent a great deal more time organizing itself because faith was shared between people, so you need everyone to believe more or less the same things.
One place where both paganism and monotheism agree is on whatever new religion is showing up. They ain't for it, whether its Dionysus worship in ancient Greece, Buddhists in China, or crystals in the Fundamentalist south. That new stuff is crazy and it'll corrupt the youth. You can guarantee some religious conflict when the new worship with its radical notions comes to town.
So as you place your characters in your stories, take a look at how they think about religion. Does belief matter? Is non-belief even possible, especially in a world where gods walk among the people? Does faith provide anything? Do some people have faith while others don't? To what extend can someone adopt or not adopt pieces of the dominant religion? How much is known or certain? How much room is there for growth and revelation?
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