Why are desktop's fan wire order GND, VCC, TACH, PWM while laptops have GND, PWM, TACH, VCC?
I believe you will find that there is no standard across devices.
Each fan in each product (computers, electronic devices and so on) all have specific replacement parts and the manufacturer will use the same coding for the specific part, but the coding need not apply to different products or manufacturers.
I looked in my Desktop computer (easy to take the side off even while running) and in some devices in my workshop.
There is no standard color coding and no standard number of wires (depends on the type of fan).
Also, in reviewing fans and the wire layout, I realized (should have thought on this already) that the fan may easily be outsourced. So manufacturer A makes the fan for manufacturer B. B tells A the orientation of the plug and the + - and possibly control wire in the plug. A send the fan to B and B plugs it in. Done.
So your question cannot be answered in the way you anticipate. There is no cross-device and cross-manufacturer standard for such a thing. A given manufacturer may (for manufacturing engineering reasons) have a color coding within a group of their own products. But that depends on the manufacturer's requirements and setups.