A person often uses a single search engine for very different tasks. For example, an author editing a manuscript may use the same academic search engine to find the latest work on a particular topic or to find the correct citation for a familiar article. The author's tolerance for latency and accuracy may vary according to task. However, search engines typically employ a consistent approach for processing all queries. In this paper we explore how a range of search needs and expectations can be supported within a single search system using differential search. We introduce CiteSight, a system that provides personalized citation recommendations to author groups that vary based on task. CiteSight presents cached recommendations instantaneously for online tasks (e.g., active paper writing), and refines these recommendations in the background for offline tasks (e.g., future literature review). We develop an active cache-warming process to enhance the system as the author works, and context-coupling, a technique for augment sparse citation networks. By evaluating the quality of the recommendations and collecting user feedback, we show that differential search can provide a high level of accuracy for different tasks on different time scales. We believe that differential search can be used in many situations where the user's tolerance for latency and desired response vary dramatically based on use.