This paper investigates how hate speech varies in systematic ways according to the identities it targets. Across multiple hate speech datasets annotated for targeted identities, we find that classifiers trained on hate speech targeting specific identity groups struggle to generalize to other targeted identities. This provides empirical evidence for differences in hate speech by target identity; we then investigate which patterns structure this variation. We find that the targeted demographic category (e.g. gender/sexuality or race/ethnicity) appears to have a greater effect on the language of hate speech than does the relative social power of the targeted identity group. We also find that words associated with hate speech targeting specific identities often relate to stereotypes, histories of oppression, current social movements, and other social contexts specific to identities. These experiments suggest the importance of considering targeted identity, as well as the social contexts associated with these identities, in automated hate speech classification