The Schelling model is a prototype for agent-based modeling in social systems. We produce a comprehensive analysis of Schelling model rule variants by classifying the space of macroscopic outcomes using phase diagrams. Among 54 rule variants, only 3 phase diagram classes are found, characterized by the number of phase transitions. This classification scheme is found to be robust to the use of sociological and percolation-inspired measures of segregation. The statistical and dynamic drivers of these transitions are elucidated by analyzing the roles of vision, movement criteria, vacancies, the initial state, and rivalry. Schelling’s original step function dictating satisfaction is found to be pathological at high thresholds, producing coordination failures as satisfactory sites become increasingly rare. This comprehensive classification gives new insight into the drivers of transitions in the Schelling model and creates a basis for studying more complex Schelling-like models.