My home is currently all ZigBee/Z-Wave, but Thread/Matter is an open protocol that can be used entirely locally. I'm cautiously excited about the industry standardizing on it; hopefully this will mean that over time more and more mainstream smart-home devices will be compatible with my local-only HomeAssistant setup.
(I honestly don't know and was thinking Matter and Thread were somehow related and the were both good and I hope someone can confirm or explain what I am missing.)
Thread is a radio protocol. It's basically next-generation Zigbee, using the same radio protocol (IEEE 802.15.4) but with higher performance, lower latency, IPv6 addressing and AES encryption.
Matter is a network protocol which provides a standard API for how smart devices talk to home hubs. By making devices truly platform agnostic, it will end the dark "Best Viewed With Internet Explorer" direction which smart devices have been going down.
I'm not sure. ZigBee is available and works great. I heard negative rumblings about Thread/Matter but I'm not sure if the criticisms are valid, or just anti-change curmudgeonry.