Quilting cottons are considered standard cottons. They have a little stretch across the bias (diagonally) and minimal stretch on the grain. This is what most people refer to when they say to use "cotton" fabric. Our most common quilting cottons are poplin and broadcloth.
Flannel is another common quilting cotton. Like poplin and broadcloth, it is a woven cotton, but flannel has nap which makes it a fuzzy and cozy fabric.
Double gauze is made from two layers of soft to the touch and soft handed cotton gauze. It is excellent for swaddling blankets, summer clothing, and even light drapes.
Swaddle is usually made from one layer of soft gauze. It has a beautiful crinkle and drape.