ZigBee adds network, application and ZigBee Device Objects (ZDOs, which define device functionality and provide security functionality) on top of the IEEE 802.15.4 PHY/MAC. The routing protocol is derived from AODV.
Zigbee works on top of the IEEE 802.15.4 standard specifications for a low power wireless personal area network. The specifications for Zigbee are available from Zigbee alliance (www.zigbee.org). There are other proprietary APIs available for Zigbee modules available in the market and they vary from one vendor to another. You can also find the specifications for 6LoWPAN (Low power wireless personal area network over IPv6) on www.ietf.org that has the necessary framework as enabling technology for Internet of Things (IoT).
Zigbee is a multi-hop extension to the IEEE 802.15.4 protocol. When we talk about IEEE 802.15.4 we talk about point to point communication though it does speak about supporting mesh protocol.
That extension to IEEE 802.15.4 is provided by Zigbee. IEEE 802.15.4 protocol define the MAC and PHY layer of the protocol while Zigbee defines the NWK and APL layer. So Zigbee works on the top of IEEE 802.15.4 protocol. Zigbee protocol is defined by the name Zigbee Specification and is openly available. AODV(its Derived AODV not the true one) is just a part of Zigbee. It handles the networking part for multi-hopping information/data.