Test Plan is a document describing an introduction to the client company, intended scope, overview of the application, test strategy, schedule of testing activities, roles and responsibilities, deliverables and milestones. It describes test items, features to be tested, testing tasks, details of the personnel performing each task and any risks requiring contingency planning.
Whereas a Use Case describes the process as to how an end user uses a specific functionality in the application. It is a summary of user actions and system response to the user actions. It contains the flows like typical flow, alternate flow and exceptional flow. It also contains pre condition and post condition.