English words with roots in the Latin, (transliterations), do NOT always conform to the original (Latin) term, but were built from them. They often have linking features, (as in your example), but not identical meanings.
For example take the word 'diversity, which means 'variety', or the respects from which things differ. It's root word is, however, divide, frm the Latin = divido = to divide up, separate into parts).
re·li·gion
Belief in and reverence for a supernatural power or powers regarded as creator and governor of the universe.
A personal or institutionalized system grounded in such belief and worship.
The life or condition of a person in a religious order.
A set of beliefs, values, and practices based on the teachings of a spiritual leader.
A cause, principle, or activity pursued with zeal or conscientious devotion.
Idiom:
get religion Informal
To become religious or devout.
To resolve to end one's immoral behavior.
Main Entry: re·li·gion
Etymology: Middle English religioun, from Latin religion-, religio supernatural constraint, sanction, religious practice, perhaps from religare to restrain,
As both of the current dictionary listings show, the broader, original Latin meaning is still valid today, along with the subset that refer to God.