“Line Shift” is how much to shift each line relative to the one before it. “Initial Offset” is how much to shift the entire engraving left or right, to align it with vectors. It’s rare that you need the Initial Offset values.
There are two things that cause scanning offsets: power supply lag and mechanical slop (backlash).
Power supply lag means that the controller tells the power supply to fire, and a millisecond or two later, it does. If you’re scanning at 500mm/sec, a two millisecond delay would be a millimeter late. For this you would use negative numbers to tell the software to start the scan earlier than usual.
Backlash is mechanical slop or looseness in the motion platform that needs to be “taken up” when you reverse direction by moving some extra amount. For this you would use positive numbers to tell the system to start scanning later than usual.