Does white balance change from lens to lens? Though I think it does not, the reason I ask is auto white balance with a wide-angle lens seems to be different from auto white balance with a macro lens. Could it be just the difference in stops of light?
Modern lenses are fabricated using an array of single element lenses. Some elements are air-spaced, some are glued together. Such a design is necessary because a single element lens suffers from a minimum of seven optical defects we call aberrations. In theory, it would take seven individual lens elements to counter these aberrations. Such an aberration free has never been achieved. Lens makers try there best, some high quality camera lens contain more than a dozen individual lens elements.
These lens elements are different as to their shape plus they are not flawlessly as to transparency. Some color is naturally inherent in the glass. Additionally, each element has two polished surfaces that reflect light. Thus as the image forming light rays traverse each element will reflect away about 2 to 3% of the wanted light. A high percentage of this stray reflected light will intermingle with the image forming light rays. This degrades the image by lowering contrast and contributing to ghost images and flare light.
The counter measure for unwanted reflections is lens coating. Each lens element is coated with a transparent covering of a specific mineral. It’s a combination of thickness and material that does this trick. The coat reduces the amount of light reflected. A single coat is specific for one color of light. A modern lens will have multiple coats, one of each color that needs to be controlled.
Bottom line, the fact that a lens consist of multiple lens elements, each with a mineral coat, adds unwanted color to the image. This tint will be compounded by the scene lighting. Often the results of a picture taking session are less than faithful because we humans see with an eye / brain combination. This human trait is imitated by the white balance routine driven by computer logic built-in the camera. When we mount a lens, its color qualities will comingle with the scene color qualities. White balance to the rescue.
I don't actually know the answer to this but would assume that each lens has differing light transmission properties such that differing tints may come through. But, aside from that, wanted to frame challenge this question a bit:
The reason I ask is my auto white balance in wide angle lens seems to be different from auto white balance when I am using a macro lens or is it just the difference in stops o light
Your wide angle lens is pulling information from a very wide scene while your macro lens a very limited scene. Your camera's AutoWB is attempting to find the exact color temperature of the light so as to set the right WB but it is doing that based on the information it sees through the lens.
If you change that scope, why would you think the AutoWB would remain the same? AutoWB can even change with the same lens from shot to shot as the camera decides the WB per shot, not per shooting session, location, or anything more complex.
So, yes, using a different lens may force your camera to interpret the WB differently, thus changing it. So too can using the same lens and shooting different subjects in the same scene.
If AutoWB were any good, we wouldn't need grey cards/color checkers/expo discs/etc. ;-)
I put two example photos there that show how drastic the change can be - mind that these are vintage lenses though.