When introduced into agile way of working I have always considered user stories as use cases and as I went about estimating and implementing these user stories, I found it out they vary a lot in nature
Easy to plan
User Stories are much easier to plan and estimate and thus forms the basis of iteration planning and is meant to implemented in a single sprint and ideally should not be carried over to the next sprint. This leads to a big advantage that can be prioritized. So a user story is much smaller in scope and lasts much shorter then a use case.
Leave the details for later
It is never meant to be always complete and more often then not are replaced by storied with greater detail when required. This enable an agile team to start with a set of broadly specified user stories to give a good idea about the application. Further the way they are made it always promote verbal communication. So a clear distinction is in the amount of completeness.
Let you be up and running very quickly
I do not have to have every single detail flushed out for a use case to start to work on it. Team can always start on one user story which make up that use case.
