Whole groats are becoming much easier to find these days. They're also processed into these common kinds of oats:
Steel-Cut Oats - We get steel-cut oats when the whole groat is split into several pieces. Simmered with water, steel-cut oats retain much of their shape and make a chewy, nutty-tasting porridge. Substitute: Whole Oat Groats
Rolled Oats - Whole grains of oats can also be steamed to make them soft and pliable, and then pressed between rollers and dried. The resulting "rolled oats" re-absorb water and cook much more quickly than whole groats or steel-cut oats. When a recipe calls for "rolled oats" or the packaging mentions it, they generally mean the thickest rolled oat, which retains its shape fairly well during cooking. Substitute: Quick oats can be substituted, but the texture will be lost
Old-Fashioned Oats - The source of much confusion, old-fashioned oats are actually the same as rolled oats. You'll usually see them called "Old-Fashioned Rolled Oats" on packaging.
Quick or Quick-Cooking Oats - These are oats that have been pressed slightly thinner than rolled oats. They cook more quickly, but retain less of their texture. Substitute: Rolled Oats or Instant Oats
Instant Oats - Pressed even thinner than quick oats, instant oats oats often break into a coarse powder. They cook the quickest of all and make a very soft and uniform mush (erm...for lack of a better description). Substitute: Quick Oats
As a final note, Harold McGee in On Food and Cooking says that all processed oats have the same nutritional value. This was a surprise to us. We assumed that the more processed the oat, the less nutrition would remain. We're happy to be proven wrong this time!
What kind of oat do you like best?
Related: Five Ways to Eat Oats