Man, I think about this a fair amount.
A lot of 20th-century modern magic is an attempt to build a ritual system that stands outside Christianity. That's a completely legitimate project, so not trying to say stop. But many of the efforts here only makes sense if you already accept the religion/magic/life split as real categories .
For most New World indigenous people there is no such thing as "religion," there is just reality. And that sense of reality can be expresses in what Anglos would call a "religion" - and sometimes more than one simultaneously, which just makes their heads pop, and smoke come out of their ears.
"Religion" as an abstract category (an "ism" among "religions") took shape only in the early modern period, especially after the Reformation, when "religion" could be reified and spoken of in the plural as "religions."
"Belief" is likewise a Middle English word from around 1175. But its original meaning differed in significant ways from our more modern understanding, and is more like... religion, but the lived, experiential kinds.
Etymologically, "believe" comes from Proto-Germanic word meaning "to hold dear" and related to love and trust, not "accepting a proposition as true with our thinky-think left-hemisphere brain," as we come to thinky-think of it
"Belief" of modern meaning of "conviction of the truth of a proposition without knowledge" emerged around the 1530s. The catalyst here was the Reformation. Protestantism emphasized the individual's "interior assent to the propositional content of doctrinal truth," while the more Catholic lived experiences of "implicit faith" was criticized as "false belief." Pfft Like get out of here kids. From then on, "belief" increasingly came to be understood as the individual mind's acceptance of certain statements, rather than a way of life embedded in ritual and community
All this is worth noticing and keep in in mind here , because the modern split between "religion" and "magic" isn't a neutral description of how people practice in the real world . It's a historically specific sorting that comes one from early modern Europe, and especially in Protestant Anglophone thought, where inward "belief"became the marker of "real religion" and outward ritual got reclassified as either superstition or magic.