Does disabling Wi-Fi prevent my smartphone from sending Wi-Fi frames?

No. For Android, we show that another option, called "Always allow scanning", when activated, makes a device send Wi-Fi frames which can be used to track this device, even if the Wi-Fi switch is off. This option is not clearly described in all Android versions, and sometimes very hard to find. Besides, the Google Maps application prompts the user to activate this option. Similarly, for iOS 11, the Wi-Fi switch in the control center does not prevent Wi-Fi frames from being emitted by some services.