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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 have 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 the functionality of the software system. In other words a written set of steps that should be performed manually.