Do these two options have a functional difference at all?
Do you have a secondary monitor? Try placing the second monitor on the left side of your main screen, and you might notice a difference between those options.
I tried that, but both options still move the mouse to the same place (I tried with coordinates of 0,0). What am I missing?
If you use the "Set variable to text" action and set is to %CurrentMouse% it always shows you the current mouse location at the bottom of the action. What do you see when you move the mouse to another screen? I cannot test it since I have only 1 screen.
I don't think you're missing anything.
Absolute coordinates are based off the top-left corner of the Main screen -- 0,0
is the same point in both schemes.
Two different references to the same system, IMO -- I can't find a practical difference. But imagine the support calls Peter would get if either weren't listed in that drop down!