AMD and NVidia do not make the cards that you buy. They only design the chips. The chips are fabricated by a ASIC fabrication company under contract (they use Taiwan Semiconductor Manufacturing Company, aka TSMC). These chips are then purchased by equipment manufacturers such as Sapphire, XFX, Gigabyte and HIS who then create the video cards based on a reference design provided by the chip designers. Some equipment manufacturers such as Asus make extensive modifications to the reference design but most don't.
By and large, there is not a huge difference between most manufacturers but some can be of much higher quality than others. Asus, Gigabyte, Sapphire, XFX and EVGA are amongst the best of the best