Use Cases. Use cases are generally written as part of detailed product requirement documentation. They capture the goal of an action, the trigger event that starts a process, and then describe each step of the process including inputs, outputs, errors and exceptions. Use cases are often written in the form of an actor or user performing an action followed by the expected system response and alternative outcomes.
Scenarios. Scenarios are generally used by user research people to communicate with design teams. They are usually tied to personas and are part of creating a story about who the user of a particular technology is, what they want, what they know. A scenario is therefore usually written in narrative form, perhaps with pictures and illustrations as well. Scenarios are generally written at the beginning of a project during discovery and requirement gathering phases.