I thought both Thread and Zigbee run on top of IEEE802.15.4, but Thread is based on 6LoWPAN / IPv6 where Zigbee uses its own network layer. But Thread idd functions fine without the internet (although you probably could connect devices to the internet if you'd want to).

Also important is that Zigbee is both the transport protocol and multiple home automational protocols. Zigbee compatibility is pretty good with the same protocol but not across different protocols.

Thread is a transport protocol for Matter home automation protocol. Matter is complex because it tries to do everything in one protocol.

Thread is based on Zigbee in the sense that the thread designers read papers about the Zigbee spec. Also matter is partially based on Zigbee with its use of Zigbee clusters (deep in the stack, away from end users).

Zigbee and thread are different protocols and incompatible. You cannot mix them and that’s what most people are about.