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It's called a wedding ring, but surely it should be called a marriage ring
(startrek.website)
A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
A wedding ring shows that you are wed. Just like an engagement ring shows that your engaged. A wedding is an event, being wed is a change in status. The logic is sound. Confusion only enters the mix, because 'being wed' is less common as a phrase than 'being married'.