Is there a difference between move next screen, and move center next screen?

They seem to behave the same on my Mac. External monitor using 1920x1080 and Laptop screen of 2880x1800. I've assigned the middle mouse button to move to the next screen and I expected it would move to the destination screen relative to where it was on the source screen. But in all cases it seems to center the window. Which appears to be exactly the same as move to the next screen and center.

(v 2.608 (912))

Move to next screen will move to the same location, but only if the monitors have the same resolution.

However I think you can use the "Custom Move / Resize" action like this: