How do I display TableView in the same way as the screen transition destination of TableView in Swift?

Since the information provided in the question does not tell you exactly what the assumptions are, I will explain how to transition to the same screen when using Storyboard and UINavigationController.

All you have to do is create and push the same ViewController when you actually transition.

func moveToNext(){
    let id = "Folder"
    let vc = storyboard ?.instantiateViewControllerWithIdentifier(id) as!UIViewController
    navigationController?pushViewController(vc, animated:true)
}

id contains the Storyboard ID specified in the Storyboard.

Also, if you manage where each screen corresponds to in the data, you will be able to edit the data on any screen.