Lets consider a library management system:

Usecase:
The functions performed by different entities(Customer, Staff, Manager) is mentioned in Usecase. a) Staff enters customer information.

Test Scenario:
Test cases are written based on scenario. Test scenarios are very brief.
a)Staff enters customer information
b)Customer returns a book

Test Cases:
Test cases are derived from scenarios. They are step by step instructions. They are very detailed and also contains actual results and expected results along with other fields
a. Enter customer information(Name, address, ph no)
b. Click on save.