[SOLVED] Xbox Series X controllers on amazon.de

Nov 1, 2020
I want to buy the new Xbox Series X controller for PC gaming. On Amazon I found two versions:
https://www.amazon.de/-/en/dp/B08JW5DR79/ - controller with wireless adapter
https://www.amazon.de/-/en/dp/B07SDFLVKD/ - only controller

Product details of the first one says:
  • Batteries : 2 AA batteries required. (included)
And of the second one:
  • Batteries : 1 Lithium ion batteries required. (included)

Is this a mistake in the description or the controllers are actually different? If so, which one will be better?