[inferiorhuman]

When you "turn off" WiFi or Bluetooth via the control center you're simply disconnecting from any remote devices. To actually turn the radio off you need to go into the WiFi or Bluetooth settings – this lasts until you turn the radios back on.

[gnicholas]

Annoyingly, I've found that it doesn't even disconnect from all currently-connected devices. For example, my AirPods are often hijacked by my iPad when I'm setting it up for my kids to watch something. To pre-empt this, I will turn off BT via Control Center, but even having done that, the AirPods often switch over. Super annoying.