You can stop the recording session by closing the browser and that should terminate the process. There is nothing else required in this case, so please let me know if there are some issue with that and I will try to help you.
The correct way to terminate a running test, is from the Abort button in the Test Studio ribbon in the Tests tab. The button appears in place of Execute button, when there is a running test. You can also close the browser to stop the test execution, but not the console window. In this case the console window will be closed automatically after a short period of time and Test Studio will be ready to execute the next test. I would recommend you to use the Abort button in all cases (see attached screenshot).
I am looking forward to hearing from you, if you need further assistance or any question arise.