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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. A showerthought should offer a unique perspective on an ordinary part of life.
I've known one woman who sometimes wore the engagement instead of the wedding ring but this was very odd and uncommon. I know everyone keeps their engagement ring but hardly anyone ever wears them, let alone on a regular basis.
I am curious what region you're from. I would guess it's outside of the US, but perhaps there's an area that differs from the norm I've experienced.
If you are indeed outside the US, I'm guessing it's the American tradition of engagement rings, without the tradition of continuing to wear the engagement rings. That truly would be a (bigger) waste of money.
You're right, I'm from Germany