The 64-bit instruction set used in both AMD and Intel CPUs now is one that was invented by AMD.
Usually known as "x86-64", it is also known sometimes as "amd64" honoring its AMD heritage, even though it is used universally by both AMD and Intel.
Both AMD and Intel originally invented their own 64-bit instruction sets. Intel's was called IA-64 (brand name "Itanium") and it failed to be successful in the consumer market. The instruction set used by both chipmakers is now the one invented by AMD. One reason AMD's version was successful was that it was backwards-compatible with 32-bit x86 software, so it could run existing operating systems available at the time.
Software vendors usually refer to it as "x86-64" now which is a less confusing term and is actually quite descriptive, because it is a 64-bit extension of the "x86" instruction set. However, the term "amd64" continues to be used by various Linux distributions like Ubuntu.