Graphics drivers for my laptop are on the sites of Nvidia or ATI.
That is rarely the case.
Nvidia and AMD/ATI are both chipset manufacturers and they publish very precise specifications for the integration of the custom products intended for laptops manufacturers and provide specific driver development.
The two founders simply provide manufacturers of notebook PC, a generic driver circuit that may be customized or adapted to fit their needs.
De facto, the PC manufacturer's site is where you should look for the right driver.