Difference Between Fat Grafting and Fat Injection?

This is a minor semantic and technical distinction.
Fat injection is a method of fat grafting.
Let me explain. Fat grafting literally means taling fat from one part of your body and transplanting it to a new location. The transferred fat (the "graft") needs to survive in it's new location and this process is referred to as the "take" of the graft.
The transferred fat can be achieved using:

injection
pearl grafting (cutting into small pearl sized pieces)
lumbrical grafts (cutting the fat into cigar shaped pieces)
dermal fat grafts (combining the fat with protions of the skin - dermis)

Surgeons may disagree on the best methods of grafting as well as the methods of processing the fat prior to transfer.

Fat grafting and fat transfer and fat injections are all the same thing. Some fat is removed from desired areas and then treated and injected into the areas that need the volume.
It can be permanent and it will be, but not all the injected fat stays. Different surgeons will quote you different percentages of how much stays. The bottom line is that you may need repeat injection to get the desired long term result that you may be looking for.
Good luck.