AMD64 (x86-64/Intel 64/EM64T/x64) - a 64-bit architecture of the microprocessor and the corresponding set of instructions developed by AMD company. This set of instructions was licensed by Intel company under the name of EM64T (Intel64). AMD64 architecture is an extension of x86 architecture with the full backward compatibility.
There are a lot of variants of the names for this architecture what causes confusion although all these names actually denote the same: x86-64, AA-64, Hammer Architecture, AMD64, Yamhill Technology, EM64T, IA-32e, Intel 64, x64. To learn in detail how so many names appeared see the article in Wikipedia: AMD64. What you should keep in mind is that Intel 64 and IA-64 are absolutely different microprocessor architectures incompatible with each other.