In simple words:
user stories are not
use cases, and
user requirements are more fine-grained document of requirements that are usually approved (or pre-approved) by client.
The user stories don’t provide the details the team needs to do their work. The Scrum process enables this detail to emerge organically, mainly by removing the need to write use cases.
Also there’s consensus that use cases and user stories are not interchangeable:
- Alistair Cockburn: A user story is to a use case as a gazelle is to a gazebo
- ExtremeProgramming.org: User stories serve the same purpose as use cases but are not the same.
- Mike Cohn: User stories aren’t use cases
You may also thing about user stories as - a short description of something that your customer will do when they come to your website or use your application/software, focused on the value or result they get from doing this thing. They are written from the point of view of a person using your website or application, and written in the language that your customers would use.
Meanwhile, use cases are more a description of a set of interactions between a system and and one or more actors (where ‘actor’ can be people, or other systems: for example, both online shoppers and PayPal can be actors). They are usually created as documents