The XBOX X/S controller
PLUG&PLAY
To use your Xbox Wireless Controller with your console after using it on PC, you'll need to re-sync the controller with the Xbox console. This can be done using the wireless sync button or a USB cable.
How does it work?
The Xbox controller provides a feature for quickly switching between a paired Bluetooth device and an Xbox console or PC using Xbox Wireless.
If the controller is connected to a Bluetooth device, double-click the pair button and the controller will immediately switch its connection back to the last Xbox Wireless connection it was paired with.
To switch back to the paired Bluetooth device, press and hold the pairing button to enter pairing mode. The controller will automatically connect to the Bluetooth device you were using while it also scans for new devices, just in case you connect another Bluetooth device, Xbox console, or PC want.
If it doesn't find a new device in pairing mode nearby, it stays connected to the previous Bluetooth device.
XBOX X/S Controller with VR possible?
Although the Oculus Rift virtual reality set is no longer manufactured or bundled with Xbox One wireless controllers, they are compatible with Windows PC and Xbox wireless controllers and can be used during game streaming. For more information, see: How to use game streaming in the Xbox Console Companion app on Windows 10.
Nice to know:
Controller vibration does not work when playing games on a PC while the controller is connected via Bluetooth. 
Xbox Series X/S Controllers:
The differences to the Xbox One predecessor
The Xbox One controller (which you can continue to use for XBOX X/S, by the way) is already one of the best game pads that you as a gamer can get your hands on. Accordingly, Microsoft is wary of making huge changes that could hamper the controller's popularity. The innovations are accordingly rather small, but fine.
The Xbox designer explains that with the new controller, Microsoft wants to focus primarily on the needs of the fans. That is why the changes are designed, among other things, to ensure that the new game pad can be used as comfortably as possible by even more people.
Small hands? No problem! This also includes the measure to make the game pad more comfortable for people with smaller hands. And without making the controller uncomfortable for people with larger hands.
D-Pad as a combination: The change in the directional pad of the new Xbox controller is perhaps the first and most noticeable: The classic directional pad now looks more like a mixture of the classic D-Pad and the recess that, for example, the Elite controller offers.
That was probably exactly the plan, as Microsoft's Ryan Whitaker reveals: to combine the best of both worlds. There is now a deeper depression in the middle where the thumb can rest. At the same time, the directions are clear and controllable with minimal effort.
Less latency: Microsoft wants to further reduce input delays, especially for fans of shooters and other games where milliseconds can matter. This works with the help of Dynamic Latency Input (DLI), a technology that ensures that information is sent back and forth more often and faster.
What's new? The following is an overview of the most important innovations:
- More comfort: even for smaller hands
- The control pad should offer "best of both worlds".
- Connectivity: more devices, easier connection
- Share button: faster & easier to share gameplay
- Less Latency: Improved response speed
- USB-C: Charge with more readily available cables
Does the Series X controller have batteries?
If you are familiar with the devices of the last console generations, you know that the controllers did not draw their energy from an internal battery, but from batteries. The Xbox Series X also keeps the batteries, so you'll still need the AA models.
Of course, you can also connect an external battery to the new device, the battery packs known from the Xbox One game pads also fit into the Xbox Series X controller.
USB-C connector or USB-A?
The controller has a USB-C port, inserted battery packs are recharged, and the controller can also be connected directly to the console via a cable.