Pima cotton is an American grown cotton recommended by Supima. Supima is the organization in charge of overseeing the distribution of American Pima cotton seed throughout the US.
When purchasing a set of sheets, consumers should always be looking for cotton products made from an extra-long staple cotton (commonly referred to as ELS cotton). The long fibers of ELS cotton make a stronger and more softer yarn, and, in turn, weave into a much stronger and softer fabric. Most high thread count sheets are made from ELS cotton because a long fiber is needed to make a very thin, yet strong, yarn.
Most cottons seen in today's marketplace are upland cotton, Pima (Supima) cotton and Egyptian cotton.
It's reasonable to assume that the lack of a "brand" (e.g. Pima cotton) means the cotton used to make the product is upland cotton. This is a shorter staple cotton and would lack the strength and consistency of the "branded" cottons. Pima cotton is a generic label (honoring the Pima Indians in the Southwest) given to any ELS cotton grown in any country from a particular type of long-staple cotton. The primary producers of Pima cotton are the U.S., Australia and Peru. Any of these producing countries can properly label their cotton: Pima.
Supima cotton is a brand name given to Pima cotton grown in the U.S. "Supima" is a licensed trademark of the Supima Association of America and exists to promote the brand. A product labeled Pima cotton might contain ELS cotton grown in the U.S. or elsewhere, but a product labeled Supima cotton must contain only ELS cotton grown in the U.S.
Egyptian cotton is a very tricky brand. It's obvious when you think about it, but any cotton grown in Egypt can rightly be labeled Egyptian cotton. Egypt is one of the largest producers of ELS cotton in the world, but not all the cotton grown in Egypt is ELS cotton. It is possible to purchase a product labeled 100% Egyptian cotton with the expectation of it being made from the very finest cotton, when in fact it could be made from lesser quality, non-ELS, Egyptian cotton. To our knowledge, there is no way for the consumer to know the true quality of the Egyptian cotton used in the manufacture of a product. What can you do? Use your judgment, and be guided by the feel of the product.
A word of caution: read the label carefully. If the label says "Pima cotton" and not "100% Pima cotton" then it is likely the Pima cotton has been blended with upland cotton. We typically assume the "100%" part when reading a label that says "Pima cotton." But, if it doesn't say 100%, don't assume 100%. The labeling used by manufacturers has become much more forthright in recent years, so more often than not you will see labeling that is very specific about the cotton content. What you read is what you get.