These two terms can be used interchangeably. Yes, I am saying there is no difference. The test case is a sequence of steps that help us perform a certain test on the application. The test script is the same thing.
Now, there is one school of thought that test case is a term used in the manual testing environment and test script is used in an automation environment. This is partly true, because of the comfort level of the testers in the respective fields and also on how the tools refer to the tests (some call test scripts and some call them to test cases). So in effect, test script and test case both are steps to be performed on an application to validate its functionality whether manually or through automation.