The reason is simple: basically either AMD or Intel does the thinking and several other companies do the manufacturing.
Think of it like the Volkswagen group. It has several companies ( audi,seat,skoda,volkswagen,porsche,etc) that sell it's products but underneath it's all basically the same.
That being said some manufacturing companies have better reputation than others Sapphire,XFX, Gigabyte and ASUS are usually well liked
No, manufacturers cater for both parties as to exclude one would be business stupidity,
And yes, as long as the graphics slot is the correct one for the card, pcie replaced agp, and so on,
so you want a card today that sits in a x16pcie slot
The platform and processor are irrelevant