Digital games have become part of the daily life of a large part of the world population, reaching audiences of different ages, genders, and cultures. Games are also becoming an increasingly explored research topic in Human-Computer Interaction (HCI), and several studies have sought to deepen the knowledge about players, identifying individual differences. Although the literature is rich in works that typify and classify players, the lack of objective comparisons can make it difficult to adopt such types to support game design or future research. Thus, this research investigates players' taxonomies and typologies regarding their motivations, behavior, and personality characteristics, analyzing how they explore these traits. We conducted a systematic mapping of the literature and analyzed 19 studies that propose or update players' types, observing how they explore the above mentioned traits. The main contribution of this paper is to offer an overview of the identified taxonomies and typologies, comparing them and mapping their attributes and applications. Such knowledge is a tool for designing games and gamified systems and can support game designers to promote engagement and motivation in complementary ways in their games. It also allows researchers and practitioners to compose a multidimensional view of the different players' types.