Not all cottons are equal but, all are made from cellulose fibers. The process that cotton goes through changes the properties.
Mercerized cotton is a stronger, smoother and shinier cotton. Mercerized cotton takes dye well. Pima, Egyptian, and Sea Island cotton usually go through a mercerization process as a result of their long fibers. Mercerized cotton is also known as pearl cotton and is pre-shrunk.
Waxed cotton can be purchased on cones. Their ability to shed water is what makes this cotton unique. Cottolin is a blend of cotton and linen. It works up to a nice crisp fabric. Click on the thumbnails to learn more about cotton fiber.
When using cotton, knit a measured swatch and wash it as the label suggests. Measure the swatch again after washing and drying. If it has shrunk, compensate by knitting the pattern larger by the percentage it shrunk. Cotton doesn't shrink very much in width but it does significantly in length. Cotton has no memory but soft drape.
If you decide to use cotton in a pattern that doesn't call for this type of yarn, understand the properties of the item you will be knitting. The more you understand about yarn, the better results you will have.