AMD only pressured Intel into adapting the 64-bit extensions to the x86 architecture, The Intel native 64-bit system was the Itanium. Which they were hoping would break x86 and it's messy open legacy that allowed AMD to profit off it.
A question on terminology, I come from bsd world so prefer i386, amd64, ia64(the itanium) whereas the linux side appears to prefer x86 x86-64 Nothing wrong with it(it describes the architecture fine) but I assume that x86-64 is intel face saving propaganda.