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Actually, long story short, what we call a x64 or 64 bits architecture is often called AMD64 in reference with the original design of the AMD K8 which is the first processor to have a 64bits x86 instruction set.
More info on: http://en.wikipedia.org/wiki/X86-64 and especially the "Industry Naming Convention" at the end.
So, you will often encounter x64 or AMD64 in computers, depending on who is making the program mentioning it.