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This is how I understand it...
I wish I had good use case examples for you. I use Relative Offset when I am blocking out a character and determining proportions. I can put an array modifier on the head in the Z axis to determine the head-height of the character. I haven't had reason to use Constant Offset that I can recall so maybe someone can pop in with a good example?
Hi Jann! Let me see if I can further demystify the difference. As Coyo said above, "relative" treats the dimension of the object as a single unit. I'll use an irregular object as an example, as a cube is the same in each dimension (X, Y and Z).
If we change the Offset to "constant" then we're telling Blender to offset the object by a distance factor. In this case, the units are set to Meters, so the Distance X is 1m. See how Suzanne - which has a dimension larger than 1 meter in the X direction - overlaps? The Object's origin is what is offset in this case.
This applies to factors in Y and Z dimensions as well. It also applies to scale and rotation.
Wait, last question. Can't I also achieve the 4m distance in constant by changing the relative offset to "2"?
The factor in any offset represents how many units. For example: 2m in Constant means 2m meters between the object origin of each instance. If the object is 2m wide, setting the relative offset to 2 would mean each instance is 4 meters apart because each factor equals 2 meters (the overall width of the object). Martin's visual above shows this clearly.
It is best not to think of a relative offset in terms of grid units. Try this: add a Suzanne. Set its array to 1 unit in Relative offset. Shrink down Suzanne. The duplicate instance should scale and also remain close to the original Suzanne. Do this with Constant, and the instance scales from its origin.
