One of my coworkers passed along some information that clears up a fine distinction regarding jewelry hardware:
An eyelet, strictly speaking, is a single-piece metal ring, reinforcing a hole in material like leather, fabric or paper. You’ll often find these in office-supply stores, craft stores and leather-working supply stores.
A grommet is bigger than an eyelet, and is two pieces (a base and a washer). It’s another way of reinforcing a hole in material with metal: the grommet base goes through a hole, the washer is placed over it and the two are affixed to each other. A specialized kind of grommet is the 
bead core, used to make a silver lining in your bead, giving a
“Pandora-style” effect.
Semi-tubular rivets look like eyelets from the back, but their tops are solid, with no hole, and are rounded. Prior to use, a semi-tubular rivet is a smooth cylindrical shaft; one end has a head on it.
🙂 And some off-subject trivia: the (usually plastic) tip at the end of a shoelace (or bolo cord) is an aglet.
Learn more about jewelry hardware here: https://www.rings-things.com/blog/riveting-101
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