Generally, most places tend to call the small ones eyelets, and the larger grommets, and both terms tend to be used interchangeably--very annoying. When purchasing, grommets are more likely to be two piece sets, and eyelets singular, but I always confirm the image or description that I am really getting two piece hardware. Lastly, single piece eyelets tend to have thinner walls, and split more easily.

To help prevent splitting, try to make sure you get ones that are higher quality material. Brass tends to be less prone to split than aluminum, for instance. And you can slow down how fast you set--setting an eyelet or grommet with one or two "Hulk smash" blows makes splitting more likely, but several lighter blows will be more likely to roll the edge back smoothly. Lastly, what are you using to set? A two piece anvil set, or a plier type tool or a press? For all setting tools, make sure the hole in your material is very tight around the eyelet or grommet, so the material supports the sidewalls. If using a two piece setter with an anvil, chose the tool set best suited for the eyelet size (don't use a 4mm tool and anvil to set 5mm eyelets or grommets), and tap lightly, especially at first, to flare the top edge of the sidewall to encourage rolling. If using pliers or a press, steadily increasing the pressure will do the same.

If using setting pliers, don't get the ones that look like a hole punch (like https://www.amazon.com/gp/aw/d/B07X9XV97Z/ref=sspa_mw_detail_2?ie=UTF8&psc=1&sp_csd=d2lkZ2V0TmFtZT1zcF9waG9uZV9kZXRhaWwp13NParams). They're nearly worthless.