Despite its often technical nature, visualization is in many ways a form of visual representation. Just how visualization relates to illustration, information graphics, digital art, visual languages, etc., is nonetheless poorly understood. We propose a theory that embeds information visualization within other visual traditions in terms of criteria that are not purely technical: dependence on data, mapping, interactivity, and notationality. In addition to providing the means for a classification, these criteria also foster a different understanding of information visualization. We further adapt our criteria to differentiate within visualization, using mapping, readability and information loss, and notationality as the criteria. Both sets of criteria are demonstrated in a number of case studies. We believe that our novel taxonomies of visualization methods serve as a step towards a more comprehensive theoretical context to understanding the essential purposes, properties, and functions of information visualization.