Hello DanXMan,
Thanks for posting your concern here.
When it comes to technical specification, Microsoft Precision Mouse and Surface Precision Mouse are actually the same and function the same. The only difference between the two is that Surface Precision Mouse is actually made and designed as a Bluetooth mouse for Surface devices bundle. Also, there is no need for you to turn off the Wi-Fi when connecting the mouse via Bluetooth. Regarding the USB functionality of the mouse, it's only compatible to devices running in Windows 7. See Precision Mouse tech specs and check Compatibility section for more details.
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Best regards,
StevenK