Requirements versus use case versus user story: see http://www.cmcrossroads.com/article/defining-requirement-types-traditional-vs-use-cases-vs-user-stories.
Important ideas:
Requirements: complete, testable, consistent (no conflicts between different requirements), design-free, unambiguous.
Use cases: describe requirements by focusing on user interaction; describe one use case as a diagram and a textual description; specify main scenario and alternative scenarios.
Req and UC focus on documented specification of the system instead on collaboration.
User stories: more narrative than req and UC; focus on the value that comes from using the system rather than a detailed specification of what the system should do.
A user story is a promise to hold a conversation.

(From http://blogs.gartner.com/donna_fitzgerald/2010/04/20/when-is-a-project-too-large-for-agile-project-management)
Question: When is a project too large for Agile project management?
Answer: Since the largest project we know about is the creation of the universe, which we have on good authority only took a single one week sprint (6 days), we think Agile PPM can scale beyond what most IT projects will ever encounter.

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