"An Intel 64 architecture processor supports existing IA-32 software because it is able to run all non-64-bit legacy modes supported by IA-32 architecture. Most existing IA-32 applications also run in compatibility mode." on page Vol.1 2-21 of Intel® 64 and IA-32 Architectures Software Developer’s Manual September 2014, which might or might not imply that Intel 64 architecture and IA-32 architecture are two things, the only link is the Intel64 processor.