Test scenario:The scenario that has to be tested,for
eg:login to the application,register for your water filter
maintenance & logout(This is the scenario)

Test case:In a step wise, each & evey instruction is written.

Test scenario:
                It tells about the work what we have to do 
for a perticular objest.

Test Case:
            It tells what work we are doing for a 
perticular objest.

Test scenario just gives an outlook of particular action to be performed where as test cases described in details how that action need to be performed. For example 

Test Scenario:-Bank account transaction 
Test case name for above test scenario are
  1. Transfer of account with minimum balance
  2. Transfer of account with maximum balance
  3. Transfer of account with any balance
  4. Transfer of account with exceed limit transfer
  5. Transfer of account in terms of decimals.
  6. Transfer of account to invalid account number
  7. Transfer of account to valid account number.


So for one scenario there can be n no. of test cases and each test cases will described how to perform such action like per supppose for 1. test case of transfer of account with minimum balance
  step 1: Login to Bank url
  step 2: Enter valid username
  step 3: Enter valid password
  step 4: Enter transfer screen
  step 5. Enter valid account number to transfer
  step 6. Enter the min amount to transfer in text field
  step 7. Enter details of account number to whom we are transfering
 step 8: click transfer
 step 9 : confirm by clicking ok
Step 10: logout of the Bank url successfully

SO for each test cases there might be such small steps to be performed .
This is test cases and if we write all test cases in above steps for each and every test cases then we can say that we have done one scenario.

 Obviously test scenario is like parent and test cases are like childrens of that parents.

Hope this will answer your question