What's the difference between a Matter controller and a Thread border router?

A Matter controller commissions and manages Matter devices on your network. A Thread border router bridges Thread's low-power mesh radio to your IP network so Thread devices can talk to controllers. Some hubs do one, some do both — the Aqara M100 and the Aqara G5 Pro line do both, while the Philips Hue Bridge is primarily a Zigbee-to-Matter bridge.