This is a second paper in a study of statistical identification and classification of earthquake clusters using a relocated catalog of 1981–2011 seismicity in southern California and synthetic catalogs produced by the Epidemic Type Aftershock Sequence model. Here we focus on classification of event families—statistically significant clusters composed of foreshocks, mainshocks, and aftershocks—that are detected with the methodology discussed in part I of the study. The families are analyzed using their representation as time oriented tree graphs. The results (1) demonstrate that the clustering associated with the largest earthquakes, m > 7, is statistically different from that of small‐to‐medium earthquakes; (2) establish the existence of two dominant types of small‐to‐medium magnitude earthquake families—burst‐like and swarm‐like sequences—and a variety of intermediate cluster forms obtained as a mixture of the two dominant types; (3) suggest a simple new quantitative measure for identifying the cluster type based on its topological structure; (4) demonstrate systematic spatial variability of the cluster characteristics on a scale of tens of kilometers in relation to heat flow and other properties governing the effective viscosity of a region; and (5) establish correlation between the family topological structure and a dozen of metric properties traditionally considered in the literature (number of aftershocks, duration, spatial properties, b‐value, parameters of Omori‐Utsu and Båth law, etc.). The burst‐like clusters likely reflect highly brittle failures in relatively cold regions, while the swarm‐like clusters are likely associated with mixed brittle‐ductile failures in regions with relatively high temperature and/or fluid content. The results of this and paper I may be used to develop improved region‐specific hazard estimates and earthquake forecasts. Key Points Four main types of earthquake clusters in southern California are detected. Earthquake cluster type is defined via topological characterization. Earthquake cluster type is related to the physical properties of the crust.