Difference between test scenarios and test cases is that
Test Scenarios: A Test Scenario is any functionality that can be tested. It is also called Test Condition or Test Possibility.
Test Cases: It is a document that contains the steps that has to be executed, it has been planned earlier.
Test Script: It is written in a programming language and it's a short program used to test part of functionality of the software system. In other words a written set of steps that should be performed manually.