Take away messages

Agile projects (especially Scrum ones) use a product backlog, which is a prioritized list of the functionality to be developed.

Product backlog items can be whatever the team desires, but user stories have emerged as the best and most popular form of product backlog items.

Both use cases and user stories focus on conversations and system usage by people.

Use cases provide more structure and a way to document details collected in analysis.

User stories are refined as needed; focus on giving an example for a small feature.