The two files are meant to split the work by what is needed to run the app as a whole and what is needed for one "instance" that would support visibly running in the background. This would be something like configuring a database once, but displaying different sets of values by window.

You could think of them as the global and private versions. One is shared and the other is limited to the individual owner. In a way, they are exactly what you would expect by the names.

Multi-window support is happening

Next time you create a new Xcode project you’ll see your AppDelegate has split in two: AppDelegate.swift and SceneDelegate.swift. This is a result of the new multi-window support that landed with iPadOS, and effectively splits the work of the app delegate in two.

From iOS 13 onwards, your app delegate should:

1. Set up any data that you need for the duration of the app.
2. Respond to any events that focus on the app, such as a file being shared with you.
3. Register for external services, such as push notifications.
4. Configure your initial scenes.

In contrast, scene delegates are there to handle one instance of your app’s user interface. So, if the user has created two windows showing your app, you have two scenes, both backed by the same app delegate.

Keep in mind that these scenes are designed to work independently from each other. So, your application no longer moves to the background, but instead individual scenes do – the user might move one to the background while keeping another open.

Courtesy of https://www.hackingwithswift.com/articles/193/whats-new-in-ios-13

AppDelegate is responsible for handling application-level events(like app launch), application lifecycle, and setup.

SceneDelegate is responsible for handling what is shown on the screen (Windows or Scenes) and managing the way your app is shown.

scene(_:willConnectTo:options:) is the first method called in UISceneSession life cycle. This method will create a new UIWindow, set the root view controller, and make this window the key window to be displayed.

application(_:didFinishLaunchingWithOptions:) is called when the application is launched and where the application set-up is done. Earlier iOS 13, we might have used this method to configure the UIWindow object and assign a ViewController instance to the UIWindow object to make it display on the screen. From iOS 13, if your application has scenes, then AppDelegate is no longer responsible for handling this and is moved to SceneDelegate.

From: https://medium.com/@kalyan.parise/understanding-scene-delegate-app-delegate-7503d48c5445

Multiplatform

In addition to the answer of Abandoned Cart, Since Xcode 11, You have a new option called Multiplatform for choosing as a starting template. That's where you will only see a file contains:

@main
struct MyMultiplatformApp: App {
    var body: some Scene {
        WindowGroup {
            ContentView()
        }
    }
}

This is how the system knows where to start the code with @main (in Swift 5.3) and it contains WindowGroup that manages multiple windows of your app in all apple platforms. So you don't need the be worry about SceneDelegate and AppDelegate anymore.

If you need it to be like the old app delegate, for example when you want to use its methods, You should subscribe for corresponding notifications or use the UIAppDelegateAdapter wrapper as I described here