Etymology: like others said, the old version of cap was short for a bullet. And that term most likely comes from “cap guns” which are/were you guys for kids that had a tiny tiny amount of gunpowder/similar so they made a small noise when fired.

So a bit of speculation, but it’s possible that the word cap has inverted twice over the years, from a toy/fake bullet, to a real bullet, and now back to being a synonym for fake, which it originally was.