The ones on the top were sold as eyelets, the ones on the bottom were sold as grommets.
A major difference when buying eyelets vs. grommets is that eyelet sizes are described just by fractions of an inch, as opposed to the grommets which usually do list the size in fractions, but also list the standard sizing. When you look at the list of the sheet metal grommets and plain washers at GrommetMart, the primary listing is the 00 through 6 size, with the size in fractions of an inch in parenthesis.
In the row of eyelets here, the first is a 1/4" Dritz eyelet from CleanerSupply, the second (the one with only one piece) is the standard 1/8" eyelet you get at any craft store and can get in all different colors, and the last one is 3/16" two-piece Dritz eyelet that I think I got at Michael's Arts and Crafts. The inner circumference of those last two seems almost the same to me, although the outer circumference on the two-part 3/16" eyelets is definitely larger. The ones from Michael's A&C have different packaging and say "The Sewing Basket," but they're still made by Dritz. I can't find them on their website; there's a Michael's next to the Lowe's around here.
The bottom row are the grommets. I don't have the tools for the first two. The first one is a 3/8" grommet from Cleaner Supply (they don't have grommets in any other size and I was having trouble picturing just how big they'd be.) The second is a size 00 grommet from corsetmaking.com and the third a size 0 from Amazon
Dfr still says that the difference is whether they're one or two piece, but if the whole row on the top is eyelets, the pieces can't be the distinguishing factor, right?
The tools are different. Grommeting tools are usually pretty expensive. The size 0 ones I got on Amazon were less than $10, but that's still more than eyelet tools usually are. The grommeting tools are bigger, and heavy. The ones for the eyelets are light and flimsy-feeling.
ETA: Okay, so it wasn't dfr. Val is the one who said the difference was 1 vs. 2 pieces.