I always thought that relative info gives us information about the object relative to the object's local coordinate system. And by this logic, if both objects have Y rotation 0, then relative rotation should give 0 in Y, as well.

Then how to understand this?

How is relative info actually converted from original info, if not by subtraction?

Here is file-example:Test

Ok, as I see, without explaining the global problem it is not very clear what I need. I'm trying to pull information about an object (loc,rot) (hereafter gradient) through an attribute from another object (hereafter controller). Obviously, the relative info of the gradient will be considered for the controller, not for the main object. So I pass the original info through the attribute, and then I need to somehow calculate the relative for the main object inside its GN. To get the same data that the object info node gives. Loc, I was already able to convert from original to relative. (Maybe I'm doing a total crap and it could be much simpler, but at least the values are the same). And the ultimate goal in general is to replicate the "Texture coordinate" Object output in GN.

Here is a new example file: Test 2