Difference between booting and mounting process of UNIX?

The 'boot' process of an Operating System brings it up from a cold or warm sequence, such as power on, or a software initiated reset. It has to bring in the software into memory and get all of the processes running. Once it is down with the 'boot' the system is ready for users to do work.

'Mounting' in Unix refers to mounting a filesystem, i.e. bringing it online for use. The system obviously has to be up and running for this to occur, so a boot process has to complete before you can mount a file system.