The .vhd format has been used with Microsoft virtualization products since the days of Virtual Server.
The .vhdx format is new to Windows Server 2012.
VHD:Virtual hard disk files in .vhd format are limited to 2040 GB. Virtual hard disks in this format are supported on Hyper-V hosts running Windows Server 2008, Windows Server 2008 R2, Windows Server 2012 and Windows Server 2012 R2.
Other than the size limitation, the important thing to remember is that you cannot use virtual hard disk files in .vhd format with generation 2 VMs.
VHDx: Virtual hard disks in .vhdx format have the following benefits:
Can be up to 64 TB in size,Have larger block size for dynamic and differential disks,Provide 4-KB logical sector virtual disks,Have an internal log that reduces chance of corruption,Support trim to reclaim unused space
The main limitation of virtual hard disks in .vhdx format is that they cannot be used with Hyper-V on Windows Server 2008 or Windows Server 2008 R2.