They are physically identical but use different wireless protocols.
| Controller | Wireless Protocol | Receiver | Works On |
|---|---|---|---|
| Xbox 360 Wireless Controller (Retail, White/Black/Special) | Proprietary 2.4 GHz (Microsoft) | Built-in (Console) / **Xbox 360 Wireless Gaming Receiver for Windows** (Black USB dongle, discontinued) | Xbox 360, PC (with Receiver) |
| Xbox 360 Wireless Controller *for Windows* (Retail Box w/ Receiver) | Proprietary 2.4 GHz (Microsoft) | **Included White USB Dongle** (same tech, different PID) | PC (with included dongle), Xbox 360 **NO** |
| Xbox 360 Wired Controller | USB 2.0 (HID) | N/A (Cable) | Xbox 360, PC, Mac, Linux, Steam Deck |
Summary: "For Windows" wireless dongle = PC only. Controller itself works wired on 360. Buy a standard wireless or wired controller for console use.