At the network level, plain Wi-Fi doesn't really cut it. To get reliable connections with lightbulbs and stuff you need a mesh network where each thing connects to nearby things and they form a network among themselves. That requires a wireless transport designed for the purpose. Zigbee is one such transport, and Thread (awful name) is a new one. Both are open standards, but the main advantage of Thread is that it doesn't need a central hub. It just needs a "border router" to talk to other networks (if things need to). Thread is based on IPv6.

At the application level, you need a protocol for controlling IoT stuff, that knows about those kinds of devices and allows an application to, for example, tell a lighbulb what colour to be. This has been done with vendor-specific protocols to date, over UDP or HTTP or whatever. Matter (also an awful name) is a new open standard for it. It can work over any IP network, including Thread ones (or WiFi or ethernet or whatever).

So between them, Matter and Thread should provide standards based connectivity and control for IoT devices, and as a key design requirement they should allow it all to work locally, i.e. without the cloud connection so many vendors have forced on people. They seem like Good Things to me.

The above is just what I've picked up and may contain inaccuracies, which I would appreciate being corrected upon.

Z-Wave has been working perfectly fine for years. There have been protocol upgrades, new hardware, a pretty large ecosystem, etc. Zigbee apparently suffers from interop problems.

It’s intended to be universal.