Raw sugar is an unregulated term, but generally refers to a brown-colored, molasses-containing sugar that is less processed than brown sugar or white sugar. Examples, depending on definition, include turbinado, demerara, sucanat, and rapadura.
Raw sugar will typically have a higher molasses content. It is nonetheless pure sugar. See: Molasses, fancy; Molasses, blackstrap; Sugar, white
Raw sugar is not a regulated term. The FDA sugar program glossary defines it as unsuitable for human consumption without further processing.