The specification for the medium access layer, or MAC, defines how multiple 802.15.4 radios operating in the same area will share the airwaves. The MAC supports several architectures, including a star topology (with one node acting as a network coordinator, much like an access point in 802.11), tree topologies (where some nodes speak through other nodes in order to arrive at the network coordinator), and mesh topologies (where nodes share routing responsibilities without the need for a master coordinator).
But just defining a PHY and a MAC doesn't guarantee that different devices will be able to talk to each other. This is where the ZigBee Alliance comes into play. ZigBee starts with the 802.15.4 standard, and is currently defining "application profiles" that will allow devices manufactured by different companies to talk to one another. For example, the ZigBee "Lighting Profile" will define all the protocols so you can purchase a ZigBee light switch from company A and know that it will work properly with lights manufactured by company B.
This was first published in April 2004