I think ZigBee uses Zig. It's an implementation.
- This thesis [1] identifies a product in this family as a Zigbee device. It's on the 80th page (numbered 62). Elsewhere it's referred to as a Zig device.
- I can't find anyone else claiming to make Zig devices or any references to a Zig protocol outside of this one manufacturer and their distributors.
- The manufacturer makes a lot of weird typos. They variously say these devices operate at 2.4GHz, 2.4MHz, and 2.4Mhz.
- There's nothing about a Zig protocol on the Zigbee Wikipedia page.
[1] https://theses.ncl.ac.uk/jspui/bitstream/10443/4329/1/Liang%...
The point is made, though: You can see how people think Zig is a protocol and Zigbee is a (certainly the primary) vendor. Whether that's true or not!