The request will be internally emulated by Laravel integrated tests and may use some advantages (like Disabling Middleware, Mocking, Spying, etc) for making sure that you are isolating a particular problem (Test Case). The goal is to test the application without introducing third party components side effects into the battlefield, this would be: the client browsers, external services, etc. These types of tests are really fast, lightweight, and very suitable for testing API calls.
So, it is not that both need to be used exclusively. They work similarly but provide different capabilities. You can have a set of Laravel integration tests, and a set of Selenium tests for those things that matter to you.