Can you please explain the differences?
These coordinate systems provide three different ways to track the machine's movements. Each has a different point of reference - or origin.
With the absolute coordinate system (shown on the absolute position display screen), the origin is the currently active program zero point. If fixture offset number one is active (machining center), then the absolute position display will show how far each axis is from the program zero point specified by fixture offset number one. This is often helpful when verifying CNC programs - you can tell from this display the tool's location relative to program zero.
This coordinate system allows you to set your own point of reference. It is most commonly used when taking measurements on the machine. With this display screen page, you can reset (set to zero) or preset (set to a specific value) the axis display registers. One example of when this display screen is needed is when measuring tool length compensation values on machining centers. During this procedure, you bring the spindle nose to a flat surface and then zero the Z axis register value (on the relative display screen page). After loading a tool, you bring the tool tip to the same surface. At this point the Z axis register of the relative page will show you the tool's length.
The origin for the machine coordinate system is the machine's zero return position - so this display screen page will always show you how far each axis is from the zero return position. It can be helpful when you're wondering whether the machine is at the zero return position (when it is, these values will be zero).