While social media empowers freedom of expression and individual voices, it also enables anti-social behavior, online harassment, cyberbullying, and hate speech. In this paper, we deepen our understanding of online hate speech by focusing on a largely neglected but crucial aspect of hate speech -- its target: either "directed" towards a specific person or entity, or "generalized" towards a group of people sharing a common protected characteristic. We perform the first linguistic and psycholinguistic analysis of these two forms of hate speech and reveal the presence of interesting markers that distinguish these types of hate speech. Our analysis reveals that Directed hate speech, in addition to being more personal and directed, is more informal, angrier, and often explicitly attacks the target (via name calling) with fewer analytic words and more words suggesting authority and influence. Generalized hate speech, on the other hand, is dominated by religious hate, is characterized by the use of lethal words such as murder, exterminate, and kill; and quantity words such as million and many. Altogether, our work provides a data-driven analysis of the nuances of online-hate speech that enables not only a deepened understanding of hate speech and its social implications but also its detection.