WiFi in a kali virtual machine?

It's probably that the interface generated inside the virtual machine is ethernet type, not wifi. With a simple command like

# ifconfig

you can see all interfaces that are up and running. Since you want to virtualbox to see it as a physical device, you must use USB device in that case, and attach it to the virtual machine from the menu.

The answer I found is a video, but it does tell you how to make this work.

Watch this video: http://www.diy-review.com/4sBQRHowToeBTE1K/Connect-USB-Wireless-Adapter-to-Kali-Linux-in-Virtualbox.html

Physically pulling the USB WIFI adapter out and re-inserting it after you've made the necessary changes in the VM settings seems to be a key component.