Use case is the way we use the application .. 
For example , for ATM application  the way we use the ATM 
machine is the use case ...

Test case is the procedure to validate whether the 
application is working properly or not .
For example we can give worng inputs and sometimes try with 
wrong usecase to findout if the ATM application is workign 
fine or not .. A test case may be written by using a use 
case also sometimes .