It is true that the three words came into the English language from the same source, Latin via Old French since you ask, and they have different meanings.
- religion - from "religare" meaning "to bind fast", the modern meaning, "recognition of, obedience to, and worship of an unseen, higher power" dates from the 1530s
- faith - from "fides" meaning "trust, reliance, credence, belief", the term entered the theological sphere in the 14th century as a synonym for "religion"
- spirituality - from "spiritualis" meaning "of concerning the spirit" though from the 14th century it meant "of concerning the church"
Personally I am convinced that faith, religion and spirituality are all one and the same thing, expressions of a human need to understand the world around them. There isn't a single human culture in history that didn't have some form of belief system to explain their environment and the things that went on within it. Religion ultimately says more about the society that created it than it does about any external deity. I suppose that is why religion is so endlessly fascinating to me, because humans are endlessly fascinating.