Are user stories (typically used in agile development or test driven development) the same thing as events in Edward Yourdon's structured analysis methodology?
A user story is a pattern for briefly describing a business, technical or other type of need. For example:
As a risk analyst I would like to add references to the application page so that we can store the references with the application, where the verifications team can then use them to help improve our risk rate in our underwriting.
Then in your user story you would decompose the story describing what tasks will be needed to complete the "would like" with a "done" check point being the "so that".
Mike Cohn has a good article on User Stories and the advantage of them http://www.mountaingoatsoftware.com/articles/27-advantages-of-user-stories-for-requirements
As far as Edward Yourdon's structured analysis methodology, I have to admit I'm not extremely familiar with it so I cant answer that part of your question.
Events and user stories are related but not identical. A Yourdon event is any stimulus to the system that requires the system to respond, so, for example, a tick from an external clock could be an event. That might require a response, eg, by incrementing a counter, but it wouldn't necessarily lead to a result with direct business value to the customer, so wouldn't be a valid user story or use case.