As it stands now. No zigbee and matter are not compatible, as zigbee has it’s own way of addressing devices (i’m not 100% clear on what they use or how it works), while matter wants to use tcp/udp. However if you have for example aqara devices that use zigbee, and you have their aqara controller, the controller will expose the devices via tcp/udp as matter devices

Matter standardises the communication. Different manufacturers can report values and controls differently for their bulbs. If the bulbs have matter support your “base station”/server can send the same “turn on/off” to the different bulbs without having code specific for that brand/model. This CAN allow us to skip brand specific bridges and such, or as in the philips hue case. All bulbs are exposed as matter devices through their bridge.