Both rolled and steel-cut oats originate from whole oat groats. What makes them different is the way they're processed. And this results in different textures and cooking times, which can make one better than the other based on your intended usage and desired outcome. They also have a few different names so let's dig in and clear things up.
Groats are the purest, least processed form of a grain, including oats. The husk is removed but the bran and germ remain, making it the longest type to cook — up to an hour. When cooked, whole oat groats have a chewy texture similar to farro and a nutty, sweet taste.
Steel-cut oats — or Irish oats — are processed a bit more. The whole toasted groats are cut into smaller pieces with a steel blade. As a result, steel-cut oats cook in about half the time of whole oat groats but still have that same chewy, subtle nutty flavor and may also be a bit creamier, especially if made overnight. They're closely related to Scottish oats, which are stone-ground instead of rolled or cut.
The classic rolled oats, aka old-fashioned oats, are steamed, rolled and flattened giving them the characteristic flat, oval shape. These are the oats of morning cereal, coffee shop muffins and late-night cookies. The unadulterated rolled oat cooks much faster — in roughly 10 minutes — and have a much softer, creamier texture when cooked. There's also the instant kind made famous by a certain Quaker that's available in individual packages and usually combined with a sugary mix of flavorings and dried fruit. These "cook" in a matter of seconds with just hot water and a microwave.