difference between Kernel version and Application ax 2012

The Dynamics AX Kernel is the component executing the X++ Application code. So the Kernel version is the version of the executable (Client, Server, Business Connectors) while the Application version is the version of the Dynamics AX “Business Logic” - the X++ Application code, Forms, Repots – everything in the AOT.
You can check the current Application version in the Dynamics AX Client going to "Help - About Microsoft Dynamics AX".