Microsoft Xbox Wi-fi Controller? – Beginner

MS appears to make use of the identical terminology for various controllers. I want an Xbox wi-fi controller to make use of with Xbox Cloud on a Samsung TV.

The $49.99 Xbox Wi-fi Controller at https://www.microsoft.com/en-us/d/xbox-wireless-controller/8xn59crbsqgz comes with two AA batteries. But MS says the Xbox Collection X|S Controller at https://assist.xbox.com/en-US/assist/hardware-network/controller/get-to-know-your-xbox-series-x-s-controller has a "USB-C energy port for charging your Xbox Collection X|S Wi-fi Controller."

1. Are these totally different controllers?
2. Does MS imply the $49.99 Xbox Wi-fi Controller can be utilized whereas gaming with both AA batteries or the USB-C energy wire?