Hyper-V is the hypervisor-based virtualization feature introduced for Windows Server 2008 server products that allows virtualization of workloads onto a single physical server. It provides a simplified, reliable and optimized virtualization solution that easily plugs into existing IT infrastructure enabling them to improve server utilization and reduce costs.
The windows azure hypervisor meants only for hardwares used in Microsoft data centers and is optimized specifically for those hardwares.